**Meet the editor**

Professor Elmer P. Dadios finished his doctoral degree at Loughborough University, United Kingdom in 1996. He was a recipient of the Philippines Department of Science and Technology (DOST) 50 Men and Women of Science and Technology; DOST Scholar Achievers); The National Research Council of the Philippines Basic Research Achievement Award; The National Academy of

Science and Technology (NAST) Outstanding Scientific Paper Award; The De La Salle University Miguel Febres Cordero Research Award. Currently, Dr. Dadios is a University Fellow of the De La Salle University and holds the University's highest faculty rank of Full Professor 10. He is the president of the NEURONEMECH Inc. He has been a consultant for Robotics and Automation in the Philippine government and private corporations. He is the founder of the IEEE Computational Intelligence Society - Philippines Chapter. He is the Founder and President of the Mechatronics and Robotics Society of the Philippines.

Contents

**Preface IX** 

**Part 1 Human Health and Security 1** 

Chapter 1 **A Clinical Application of Fuzzy Logic 3** 

Andera Pella, Ali Negarestani,

Chapter 2 **A Fuzzy Logic Approach for Remote** 

Jasenka Gajdoš Kljusurić,

**Neuro-Fuzzy Networks** 

**for Accident Black Spot Centers Determination 83** 

Chapter 5 **Fuzzy Clustering Approach** 

Yetis Sazi Murat

Chapter 6 **Adaptive Security Policy Using** 

Chapter 4 **Fuzzy Logic and** 

Ahmad Esmaili Torshabi, Marco Riboldi,

Mohamad Rahnema and Guido Baroni

**Healthcare Monitoring by Learning** 

Chapter 3 **Application of Fuzzy Logic in Diet Therapy – Advantages of Application 41** 

Ivana Rumora and Želimir Kurtanjek

Ignazio M. Mancini, Salvatore Masi, Donatella Caniani and Donata S. Lioi

**User Behavior Analysis and Human Elements of Information Security 99**  Ines Brosso and Alessandro La Neve

Hamid Medjahed, Dan Istrate, Jérôme Boudy, Jean Louis Baldinger, Lamine Bougueroua, Mohamed Achraf Dhouib and Bernadette Dorizzi

**for Environmental Hazard Assessment 65** 

**and Recognizing Human Activities of Daily Living 19** 

### Contents

#### **Preface XI**

**Part 1 Human Health and Security 1**  Chapter 1 **A Clinical Application of Fuzzy Logic 3**  Ahmad Esmaili Torshabi, Marco Riboldi, Andera Pella, Ali Negarestani, Mohamad Rahnema and Guido Baroni Chapter 2 **A Fuzzy Logic Approach for Remote Healthcare Monitoring by Learning and Recognizing Human Activities of Daily Living 19**  Hamid Medjahed, Dan Istrate, Jérôme Boudy, Jean Louis Baldinger, Lamine Bougueroua, Mohamed Achraf Dhouib and Bernadette Dorizzi Chapter 3 **Application of Fuzzy Logic in Diet Therapy – Advantages of Application 41**  Jasenka Gajdoš Kljusurić, Ivana Rumora and Želimir Kurtanjek Chapter 4 **Fuzzy Logic and Neuro-Fuzzy Networks for Environmental Hazard Assessment 65**  Ignazio M. Mancini, Salvatore Masi, Donatella Caniani and Donata S. Lioi Chapter 5 **Fuzzy Clustering Approach for Accident Black Spot Centers Determination 83**  Yetis Sazi Murat Chapter 6 **Adaptive Security Policy Using User Behavior Analysis and Human Elements of Information Security 99** 

Ines Brosso and Alessandro La Neve

X Contents


### Preface

For the past years, the advancement and innovation of various fields of technology converge that resulted in the formation of emerging technologies. A technical innovation which represents progressive developments within a field of competitive advantage is considered as an emerging technology. In general, emerging technologies denote significant technology developments that capture new territory for the betterment of humanity. To date, creating new technologies and innovative algorithms is the focus of research and development. Fuzzy logic system is one of the innovative algorithms that showed promising results in developing emerging technologies.

Fuzzy logic was first proposed in 1965 by Lotfi A. Zadeh of the University of California at Berkeley. Fuzzy logic is based on the idea that humans do not think in terms of crisp numbers, but rather in terms of concepts. The degree of membership of an object in a concept may be partial, with an object being partially related with many concepts. By characterizing the idea of partial membership in concepts, fuzzy logic is better able to convert natural language control strategies used by humans in a form usable by machines. The application of fuzzy logic in control problem was first introduced by Mamdani in 1974.

This book presents fuzzy logic applications to Emerging Technologies. It is categorized into three sections namely:


In section one, there are four chapters that focus on human health, particularly:


and two chapters that focus on human security, namely:

	- 1. Fuzzy Clustering Approach for Accident Black Spot Centers Determination
	- 2. Adaptive Security Policy using User Behavior Analysis and Human Elements of Information Security

In section two, there are three chapters that focus on transportation, particularly:


and three chapters that focus on communication, as follows:


Finally, section three consists of four chapters dedicated to Business, Environment and Energy, particularly:


The contributions to this book clearly reveal the importance and effectiveness of fuzzy logic algorithm to the development of emerging technologies. The readers will find this book a unique and significant source of knowledge and reference for the years to come.

> **Elmer P. Dadios**  University Fellow and Full Professor, Department of Manufacturing Engineering and Management, De La Salle University Philippines

## **Part 1**

**Human Health and Security** 

**1** 

*1Iran 2Italy* 

**A Clinical Application of Fuzzy Logic** 

*2Bioengineering Unit, Centro Nazionale di Adroterapia Oncologica, Pavia,* 

In fuzzy logic, linguistic variables are used to represent operating parameters in order to apply a more human-like way of thinking [Zadeh, 1965, 1968, 1973, 1988, 1989]. Fuzzy logic incorporates a simple, *IF-THEN rule-based* approach to solve a problem rather than attempting to model a system mathematically and this property plays a central role in most of fuzzy logic applications [Kang et al., 2000; Lin & Wang, 1999; Shi et al., 1999]. Recently, the main features of fuzzy logic theory make it highly applicable in many systematic designs in order to obtain a better performance when data analysis is too complex or impractical for conventional mathematical models. This chapter represents how fuzzy logic, as explained theoretically in the previous chapters, can practically be applied on a real case. For this aim, a clinical application of fuzzy logic was taken into account for cancer treatment by

Cancer is an inclusive phrase representing a large number of deseases in which unconrolled cells are divided and grown out of regular form and also are able to invade other healthy tissues. Cancer can usually be treated using surgery, chemotherapy or radiotherapy [Cassileth & Deng, 2004; Smith, 2006; Vickers, 2004]. In radiotherapy method the cancerious cells are bombarded by high energy ionizing radiation such as gamma ray or charge particle beams. The radiation ionizes the bonds of water molecoules located in cell environment and causes releasing of hydroxyl free radicals that have damaging effects for DNA. In external radiotherapy the first and most important step is tumor localization for obtaining maximum targeting accuracy. Tumor volume is visualized using 3D imaging systems [Balter & Kessler 2007; Evans, 2008] such as Computed Tomography (CT) or Magnetic Resonance Imaging (MRI) and then the contoured treatment region depicted by medical physicists is irradiated by means of an external beam extracted from the accelerator systems. In radiotherapy the correct and accurate information of tumor position during the treatment determine the degree of treatment success. Among different tumors, some typical tumors located in lung region of patient body move due to breathing cycle phenomena and this non-regular motion

**1. Introduction** 

developing a fuzzy correlation model.

Ahmad Esmaili Torshabi1, Marco Riboldi2,

Mohamad Rahnema1 and Guido Baroni2

*Kerman Graduate University of Technology, Kerman,* 

Andera Pella2, Ali Negarestani1,

*1Department of Electrical & Computer,* 

## **A Clinical Application of Fuzzy Logic**

Ahmad Esmaili Torshabi1, Marco Riboldi2, Andera Pella2, Ali Negarestani1, Mohamad Rahnema1 and Guido Baroni2 *1Department of Electrical & Computer, Kerman Graduate University of Technology, Kerman, 2Bioengineering Unit, Centro Nazionale di Adroterapia Oncologica, Pavia, 1Iran 2Italy* 

#### **1. Introduction**

In fuzzy logic, linguistic variables are used to represent operating parameters in order to apply a more human-like way of thinking [Zadeh, 1965, 1968, 1973, 1988, 1989]. Fuzzy logic incorporates a simple, *IF-THEN rule-based* approach to solve a problem rather than attempting to model a system mathematically and this property plays a central role in most of fuzzy logic applications [Kang et al., 2000; Lin & Wang, 1999; Shi et al., 1999]. Recently, the main features of fuzzy logic theory make it highly applicable in many systematic designs in order to obtain a better performance when data analysis is too complex or impractical for conventional mathematical models. This chapter represents how fuzzy logic, as explained theoretically in the previous chapters, can practically be applied on a real case. For this aim, a clinical application of fuzzy logic was taken into account for cancer treatment by developing a fuzzy correlation model.

Cancer is an inclusive phrase representing a large number of deseases in which unconrolled cells are divided and grown out of regular form and also are able to invade other healthy tissues. Cancer can usually be treated using surgery, chemotherapy or radiotherapy [Cassileth & Deng, 2004; Smith, 2006; Vickers, 2004]. In radiotherapy method the cancerious cells are bombarded by high energy ionizing radiation such as gamma ray or charge particle beams. The radiation ionizes the bonds of water molecoules located in cell environment and causes releasing of hydroxyl free radicals that have damaging effects for DNA. In external radiotherapy the first and most important step is tumor localization for obtaining maximum targeting accuracy. Tumor volume is visualized using 3D imaging systems [Balter & Kessler 2007; Evans, 2008] such as Computed Tomography (CT) or Magnetic Resonance Imaging (MRI) and then the contoured treatment region depicted by medical physicists is irradiated by means of an external beam extracted from the accelerator systems. In radiotherapy the correct and accurate information of tumor position during the treatment determine the degree of treatment success. Among different tumors, some typical tumors located in lung region of patient body move due to breathing cycle phenomena and this non-regular motion

A Clinical Application of Fuzzy Logic 5

W LLL 96.9 70.5 75.7 31.9 11.3 12.6 41.0 59.2 97.8 W RLL 14.8 28.4 11.8 24.3 7.9 12.9 57.2 33.8 38.1 W LLL 20.3 45.9 12.9 7.8 7.5 5.7 53.2 44.1 93.1 W LLL 20.2 54.1 9.2 4.6 6.4 7.7 65.2 42.4 93.5 W LEFT LUNG 95.9 23.4 24.5 37.2 6.2 10.5 67.5 29.6 27.0

ARTERY 8.6 9.1 33.5 20.1 5.9 11.7 63.7 62.1 87.1

HILUM 1.4 18.2 12.4 7.7 1.8 1.9 73.7 38.2 61.4

6.0 2.0 3.5 4.3 0.9 0.4 81.7 32.8 61.3

C LLL 2.7 23.8 3.1 1.8 1.7 1.2 65.1 32.0 68.3 C CHESTWALL 1.9 2.6 3.2 7.7 1.4 0.9 63.6 31.7 59.4 C LIVER 5.5 18.7 3.3 7.8 1.2 0.7 64.5 29.1 41.9 C RUL 5.8 4.0 1.8 6.4 1.2 0.7 97.6 44.1 70.0

C LEFT FLANK 1.6 3.0 2.2 2.4 0.5 0.3 58.1 26.0 69.7

One of the main factors affected on fuzzy model performance is data clustering for membership function generation [Jain et al., 1999]. Two most practical data clustering approaches considered in this chapter are Subtractive and Fuzzy C-Means (FCM) clustering

In this chapter fuzzy model structure and different steps of model performance were explained graphically and finally we compared fuzzy model performance with two different correlation models based on Artificial Neural Network and State model [Procházka & Pavelka, 2007; Robert et al., 2002; Ruan et al., 2008; Seppenwoolde et al., 2007; Sharp et al., 2004; Su et al., 2005]. The state model was implemented as a linear/quadratic correlation between external marker motion and internal tumor motion. In this model The 3D

\*\* LLL, RLL and RUL indicate Left Lower Lung, Right Lower Lung and Right Upper Lung,

W LEFT LUNG 27.0 55.8 25.8 40.7 5.5 6.1 71.9 59.8 105.4 W RIGHTLUNG 29.2 17.3 4.4 6.2 5.4 7.3 61.7 25.6 38.5 W LLL 23.6 32.4 14.5 16.8 5.1 4.9 61.2 50.8 85.7 W RUL 12.2 24.7 18.9 21.2 5.0 3.6 75.1 54.2 118.8 C RLL 3.4 31.1 5.0 3.8 3.2 3.2 66.9 33.1 78.0 C LLL 4.4 11.6 6.1 10.2 2.7 1.1 81.7 32.1 68.1 C PANCREAS 3.3 15.8 15.9 12.0 2.2 2.3 55.8 33.0 90.1

**Synchrony® Error [mm]** 

**Imaging intervals [s]**  **Treatment time [min]** 

**Tumor motion [mm]** 

SI LR AP Mean STD Mean STD

**Ext motion [mm]** 

**Case\* Site** 

<sup>W</sup>LEFT LUNG

<sup>C</sup>RIGHT

LEFT SPLENIC BED

\*W and C denote worst and control cases, respectively

Table 1. Features of the cases selected for this study.

[Bezdek, 1981; Chiu, 1994; Dunn, 1973; Jang et al., 1997].

C

correspondingly

causes a constraint to achieve the accurate knowledge of tumor location during the treatment [Ramrath et al., 2007; Vedam et al., 2004]. In order to address this issue, one strategy is tracking the tumor motion by continuous monitoring systems such as fluoroscopy which is unsafe for patient due to its additional exposed dose [Dieterich et al., 2008; Keall etal., 2006]. Another alternative that is effective and acceptable, is finding real time tumor position information over time from external rib cage motion [Torshabi et al., 2010]. For this aim, the external breathing motion is synchronized and correlated with internal tumor motion by developing a correlation model in training step before the treatment. It should be mentioned that the external breathing motion is traced by means of specific external markers placed on thorax region (rib cage and abdomen) of patient and recorded by infrared tracking system. In contrast, the internal tumor motion is tracked using implanted internal clips inside or near the tumor volume and visualized using orthogonal X-ray imaging in snapshot mode. A correlation model based on fuzzy logic concept is proposed here to estimate the tumor motion from external markers data as input data when internal marker data is out of access. In order to investigate the clinical application of fuzzy logic, data from real patients were utilized for model testing and verification (Table 1). The end result is a nonlinear mapping from the motion data of external markers as input to an output which is the estimate of tumor motion. When tumor position was predicted by fuzzy model, the gated-respiratory radiotherapy can be applied to treat the tumor [Kubo & Hill 1996, Minohara et al. 2000, Ohara et al., 1989]. In this method the therapeutic beam is only ON in a pre-defined gating window in which tumor volume exists and otherwise, the beam is set to turn OFF for preventing healthy tissues against additional exposure. Therefore based on above description, the specific clinical application of fuzzy model in this chapter consists of all moving targets located in thorax region of patient body such as lung, chestwall and pancreas cancers.

Recently, several respiratory motion prediction models have been developed in different mathematical approaches [Kakar et al., 2005; Murphy et al., 2006; Ramarth et al., 2007; Riaz et al., 2009; Ruan et al., 2008; Vedam et al., 2004]. Since the breathing phenomenon has inherently high uncertainty and therefore causes a significant variability in input/output dataset, fuzzy logic seems to have suitable environment to correlate input data with tumor motion estimation with less error [Kakar et al., 2005; Torshabi et al., 2010].

Our patient database consists of a real database obtained from 130 patients, who received hypo-fractionated stereotactic body radiotherapy with CyberKnife® (Accuray Inc., Sunnyvale, CA) between 2005 and 2007, was analyzed [Brown et al., 2007; Hoogeman et al., 2009; Seppenwoolde et al., 2007]. The patient database is made available by the Georgetown University Medical Center (Washington, DC). Such database includes patients treated with real-time compensation of tumor motion by means of the Synchrony® respiratory tracking module, as available in the Cyberknife® system. This system provides tumor tracking relying on an external/internal correlation model between the motion of external infrared markers and of clips implanted near the tumor. The model is built at the beginning of each irradiation session and updated as needed over the course of treatment. Twenty patients were selected randomly among the population, as shown in table 1. The chosen patients were divided into control and worst groups and the 3D targeting error of each group were analyzed, separately. The worst group consists of tumor motions with large tracking error.

causes a constraint to achieve the accurate knowledge of tumor location during the treatment [Ramrath et al., 2007; Vedam et al., 2004]. In order to address this issue, one strategy is tracking the tumor motion by continuous monitoring systems such as fluoroscopy which is unsafe for patient due to its additional exposed dose [Dieterich et al., 2008; Keall etal., 2006]. Another alternative that is effective and acceptable, is finding real time tumor position information over time from external rib cage motion [Torshabi et al., 2010]. For this aim, the external breathing motion is synchronized and correlated with internal tumor motion by developing a correlation model in training step before the treatment. It should be mentioned that the external breathing motion is traced by means of specific external markers placed on thorax region (rib cage and abdomen) of patient and recorded by infrared tracking system. In contrast, the internal tumor motion is tracked using implanted internal clips inside or near the tumor volume and visualized using orthogonal X-ray imaging in snapshot mode. A correlation model based on fuzzy logic concept is proposed here to estimate the tumor motion from external markers data as input data when internal marker data is out of access. In order to investigate the clinical application of fuzzy logic, data from real patients were utilized for model testing and verification (Table 1). The end result is a nonlinear mapping from the motion data of external markers as input to an output which is the estimate of tumor motion. When tumor position was predicted by fuzzy model, the gated-respiratory radiotherapy can be applied to treat the tumor [Kubo & Hill 1996, Minohara et al. 2000, Ohara et al., 1989]. In this method the therapeutic beam is only ON in a pre-defined gating window in which tumor volume exists and otherwise, the beam is set to turn OFF for preventing healthy tissues against additional exposure. Therefore based on above description, the specific clinical application of fuzzy model in this chapter consists of all moving targets located in thorax region of patient body such as lung,

Recently, several respiratory motion prediction models have been developed in different mathematical approaches [Kakar et al., 2005; Murphy et al., 2006; Ramarth et al., 2007; Riaz et al., 2009; Ruan et al., 2008; Vedam et al., 2004]. Since the breathing phenomenon has inherently high uncertainty and therefore causes a significant variability in input/output dataset, fuzzy logic seems to have suitable environment to correlate input data with tumor

Our patient database consists of a real database obtained from 130 patients, who received hypo-fractionated stereotactic body radiotherapy with CyberKnife® (Accuray Inc., Sunnyvale, CA) between 2005 and 2007, was analyzed [Brown et al., 2007; Hoogeman et al., 2009; Seppenwoolde et al., 2007]. The patient database is made available by the Georgetown University Medical Center (Washington, DC). Such database includes patients treated with real-time compensation of tumor motion by means of the Synchrony® respiratory tracking module, as available in the Cyberknife® system. This system provides tumor tracking relying on an external/internal correlation model between the motion of external infrared markers and of clips implanted near the tumor. The model is built at the beginning of each irradiation session and updated as needed over the course of treatment. Twenty patients were selected randomly among the population, as shown in table 1. The chosen patients were divided into control and worst groups and the 3D targeting error of each group were analyzed, separately. The worst group consists of tumor motions with large tracking error.

motion estimation with less error [Kakar et al., 2005; Torshabi et al., 2010].

chestwall and pancreas cancers.


\*W and C denote worst and control cases, respectively

\*\* LLL, RLL and RUL indicate Left Lower Lung, Right Lower Lung and Right Upper Lung, correspondingly

Table 1. Features of the cases selected for this study.

One of the main factors affected on fuzzy model performance is data clustering for membership function generation [Jain et al., 1999]. Two most practical data clustering approaches considered in this chapter are Subtractive and Fuzzy C-Means (FCM) clustering [Bezdek, 1981; Chiu, 1994; Dunn, 1973; Jang et al., 1997].

In this chapter fuzzy model structure and different steps of model performance were explained graphically and finally we compared fuzzy model performance with two different correlation models based on Artificial Neural Network and State model [Procházka & Pavelka, 2007; Robert et al., 2002; Ruan et al., 2008; Seppenwoolde et al., 2007; Sharp et al., 2004; Su et al., 2005]. The state model was implemented as a linear/quadratic correlation between external marker motion and internal tumor motion. In this model The 3D

A Clinical Application of Fuzzy Logic 7

Fig. 1. Block diagram of fuzzy inference system (lower part) and data clustering algorithm

Between several techniques for data clustering, two of most representative techniques utilized in our model are: 1) Subtractive clustering, 2) Fuzzy C-Means clustering. In the training step, two fuzzy inference systems based on above clustering approaches are configured for motion prediction during the treatment. The properties and implementations

The first clustering algorithm employed for data grouping in this work is on the basis of subtractive technique. In this algorithm, each data point of the dataset is assumed as potential cluster center and therefore a *density measure* at data point *ai* is calculated as the

(upper part)

following equation:

Fig. 2. Flowchart of correlation model performance

of these inference systems are in the following paragraphs.

**2.1 Membership function generation via subtractive clustering** 

movement of external markers was transformed into a mono-dimensional signal, by projecting the three-dimensional coordinates in the principal component space [Ruan et al., 2008]. Artificial Neural Networks (ANNs) are a mathematical method that simulates the behavior of a natural neural network, where several inputs are integrated to obtain outputs according to predefined rules. The nodes (synapses) are inter-connected with specific weight values, defined during the training phase and representing the significance of each connection. ANNs are widely used to predict signals that may be difficult to model.

The analyzed results of 3D targeting error assessment onto two control and worst groups represent that the implemented fuzzy logic-based correlation model represents the best performance rather than two alternative modelers. In general, fuzzy logic theory appears very useful when the process to be modeled is too complex for conventional techniques, or when the available dataset can be interpreted either qualitatively or with a large degree of uncertainty. Final verifications represent that this model can be potentially applicable for moving tumor located in lung and abdominal region of patient body as some typical cases depicted in table 1.

#### **2. Development of fuzzy correlation model**

In fuzzy logic-based systems, membership functions represent the magnitude of participation of each input, graphically. The proposed fuzzy correlation model involves data clustering [Jain et al., 1999] for membership function generation, as inputs for fuzzy inference system section (Figure 1, upper solid rectangle). Data clustering is an approach for finding similar data in a big dataset and puting them into a group. In the other word, data clustering analysis is the organization of a collection of dataset into clusters based on similarity. Therefore, clustering divides a dataset into several groups such that each group consists of a set of data points with same nature. the main purpose of data clustering is breaking a huge dataset into some small groups in order to make a further simplification for data analysis. Clustering algorithms are utilized not only to categorize the data but are also helpful for data compression and model construction. In some cases data clustering can discover a relevance knowledge among datapoints with same nature [Azuaje et al., 2000]. In the implemented fuzzy logic algorithm, data from all three external markers arranged in an input matrix with 9 columns and data from internal marker set in an output matrix with 1 column are clustered initially. Sugeno and Mamdani types of Fuzzy Inference Systems configured by 1) data fuzzification, 2) *if-then* rules induction, 3) application of implication method, 4) output aggregation and 5) defuzzification steps, utilized due to its specific effects on model performance (Figure 1, upper solid rectangles).

Fuzzy correlation model was developed in MatLab (The MathWorks Inc., Natick, MA, USA) using fuzzy logic toolbox. The model is built before the treatment using training data. Training data is 3D external markers motion as model input and internal implanted marker as model output. When the model is developed, it can be applied to estimate tumor motion as a function of time during the treatment (figure 2, solid blocks). The model can also be updated and re-built as needed during the treatment with X-ray imaging representing the internal marker location. Figure 2 shows a block diagram of model operation. The dashed rectangles (right side) in this figure represent the training and updating steps.

movement of external markers was transformed into a mono-dimensional signal, by projecting the three-dimensional coordinates in the principal component space [Ruan et al., 2008]. Artificial Neural Networks (ANNs) are a mathematical method that simulates the behavior of a natural neural network, where several inputs are integrated to obtain outputs according to predefined rules. The nodes (synapses) are inter-connected with specific weight values, defined during the training phase and representing the significance of each

The analyzed results of 3D targeting error assessment onto two control and worst groups represent that the implemented fuzzy logic-based correlation model represents the best performance rather than two alternative modelers. In general, fuzzy logic theory appears very useful when the process to be modeled is too complex for conventional techniques, or when the available dataset can be interpreted either qualitatively or with a large degree of uncertainty. Final verifications represent that this model can be potentially applicable for moving tumor located in lung and abdominal region of patient body as some typical cases

In fuzzy logic-based systems, membership functions represent the magnitude of participation of each input, graphically. The proposed fuzzy correlation model involves data clustering [Jain et al., 1999] for membership function generation, as inputs for fuzzy inference system section (Figure 1, upper solid rectangle). Data clustering is an approach for finding similar data in a big dataset and puting them into a group. In the other word, data clustering analysis is the organization of a collection of dataset into clusters based on similarity. Therefore, clustering divides a dataset into several groups such that each group consists of a set of data points with same nature. the main purpose of data clustering is breaking a huge dataset into some small groups in order to make a further simplification for data analysis. Clustering algorithms are utilized not only to categorize the data but are also helpful for data compression and model construction. In some cases data clustering can discover a relevance knowledge among datapoints with same nature [Azuaje et al., 2000]. In the implemented fuzzy logic algorithm, data from all three external markers arranged in an input matrix with 9 columns and data from internal marker set in an output matrix with 1 column are clustered initially. Sugeno and Mamdani types of Fuzzy Inference Systems configured by 1) data fuzzification, 2) *if-then* rules induction, 3) application of implication method, 4) output aggregation and 5) defuzzification steps, utilized due to its specific effects

Fuzzy correlation model was developed in MatLab (The MathWorks Inc., Natick, MA, USA) using fuzzy logic toolbox. The model is built before the treatment using training data. Training data is 3D external markers motion as model input and internal implanted marker as model output. When the model is developed, it can be applied to estimate tumor motion as a function of time during the treatment (figure 2, solid blocks). The model can also be updated and re-built as needed during the treatment with X-ray imaging representing the internal marker location. Figure 2 shows a block diagram of model operation. The dashed

rectangles (right side) in this figure represent the training and updating steps.

connection. ANNs are widely used to predict signals that may be difficult to model.

depicted in table 1.

**2. Development of fuzzy correlation model** 

on model performance (Figure 1, upper solid rectangles).

Fig. 1. Block diagram of fuzzy inference system (lower part) and data clustering algorithm (upper part)

Fig. 2. Flowchart of correlation model performance

Between several techniques for data clustering, two of most representative techniques utilized in our model are: 1) Subtractive clustering, 2) Fuzzy C-Means clustering. In the training step, two fuzzy inference systems based on above clustering approaches are configured for motion prediction during the treatment. The properties and implementations of these inference systems are in the following paragraphs.

#### **2.1 Membership function generation via subtractive clustering**

The first clustering algorithm employed for data grouping in this work is on the basis of subtractive technique. In this algorithm, each data point of the dataset is assumed as potential cluster center and therefore a *density measure* at data point *ai* is calculated as the following equation:

A Clinical Application of Fuzzy Logic 9

*N*

*=i*

1

*j*

efficient and thus gives a faster response, where quick decisions should be taken.

between 0 and 1, U is [uij] matrix and k is the number of iterations.

rules connected with AND operator, have been utilized.

*=c*

*m ij*

*u*

*xu*

*i m ij*

*=i*

This iteration process will continue till |U(k+1)-U(k)|<ε, where ε is a termination criterion

In should be noted that the structure of fuzzy inference systems is based on Sugeno (or Takagi-Sugeno-Kang) model [Sugeno & Takagi, 1985]. This model is computationally more

For better description, a typical fuzzy inference system on the basis of FCM clustering algorithm was built as example using the data of one chosen patient from table one with Right Lower Lung (RLL) cancer. Figure 3-a shows a set of Gaussian membership functions generated by this fuzzy inference system on input data given by three external markers that move on three X, Y and Z directions (totally 9 inputs) and figure 3-b illustrates the same membership functions using the same algorithm on output data given by implanted internal marker only on X direction. In this inference system three clusters and hence three *if-then*

1

 *N*

$$DM\_j = \sum\_{i=1}^{m} \exp\left(-\frac{\left\|a\_i - c\_j\right\|^2}{(r/2)^2}\right)$$

Where *ai* is the *i*th measured data point, *cj* is the center of the cluster, and *r* is the neighborhood radius or influence range. By this way, when density value of a data point is high, that data point is surrounded by a huge amount of other neighboring data points.

Subtractive clustering algorithm firstly nominates a datapoint as first cluster center such that its density value calculated by above formula is the largest. As the second step, the algorithm removes all data points belonging to the first cluster, configured with a predefined neighboring radius for determining the next data cluster and its center location. In the third and last step, this clustering algorithm continues density measurements on the rest of data points until all the data points are covered by the sufficient clusters. By ending these steps and when all of data were categorized, a set of fuzzy rules and membership functions are resulted.

#### **2.2 Membership function generation via Fuzzy C-Means clustering**

In Fuzzy C-Means clustering algorithm each data point in the dataset belongs to every cluster with a specific membership degree. The magnitude of this membership degree is determined by finding the distance of data point from cluster center. In the other word, each data point that is close to the cluster center has high value of membership degree, otherwise if a data point that lies far away from the cluster center has a low membership degree. It should be noted that in this way, before applying FCM technique our training dataset is clustered into *n* groups using subtractive clustering algorithm, as mentioned previously.

From mathematical point of view, membership functions in FCM clustering algorithm are obtained by minimization of the following objective function. This equation represents the distance from any given data point to a cluster center weighted by its membership degree:

$$J\_m = \sum\_{i=1}^N \sum\_{j=1}^C \mu\_{ij}^m \left| \mathbf{x}\_i - \mathbf{c}\_j \right|^2$$

where *m* is any real number greater than 1, *uij* is the degree of membership of *xi* in cluster *j*, *xi* is the *i*th measured data point, and *cj* is the center of the cluster. The value of *m* was set to 2 in our objective function [Bedzek & Pal 1998; Yu 2004]. At first, FCM assumes the cluster centers in the mean location of each cluster. Next, the FCM algorithm sets a membership degree for each data point at each cluster, and then iteratively moves the cluster centers *cj* and updates the membership degrees *uij*:

$$\mu\_{ij} = \frac{1}{\sum\_{k=1}^{c} \left( \frac{|\mathbf{x}\_i - \mathbf{c}\_j|}{|\mathbf{x}\_i - \mathbf{c}\_k|} \right)^2}$$

 

*m*

*=i*

1

*j*

*=DM*

**2.2 Membership function generation via Fuzzy C-Means clustering** 

are resulted.

Where *ai* is the *i*th measured data point, *cj* is the center of the cluster, and *r* is the neighborhood radius or influence range. By this way, when density value of a data point is high, that data point is surrounded by a huge amount of other neighboring data points.

Subtractive clustering algorithm firstly nominates a datapoint as first cluster center such that its density value calculated by above formula is the largest. As the second step, the algorithm removes all data points belonging to the first cluster, configured with a predefined neighboring radius for determining the next data cluster and its center location. In the third and last step, this clustering algorithm continues density measurements on the rest of data points until all the data points are covered by the sufficient clusters. By ending these steps and when all of data were categorized, a set of fuzzy rules and membership functions

In Fuzzy C-Means clustering algorithm each data point in the dataset belongs to every cluster with a specific membership degree. The magnitude of this membership degree is determined by finding the distance of data point from cluster center. In the other word, each data point that is close to the cluster center has high value of membership degree, otherwise if a data point that lies far away from the cluster center has a low membership degree. It should be noted that in this way, before applying FCM technique our training dataset is clustered into *n* groups using subtractive clustering algorithm, as mentioned previously.

From mathematical point of view, membership functions in FCM clustering algorithm are obtained by minimization of the following objective function. This equation represents the distance from any given data point to a cluster center weighted by its membership degree:

*N*

*C*

*=j*

where *m* is any real number greater than 1, *uij* is the degree of membership of *xi* in cluster *j*, *xi* is the *i*th measured data point, and *cj* is the center of the cluster. The value of *m* was set to 2 in our objective function [Bedzek & Pal 1998; Yu 2004]. At first, FCM assumes the cluster centers in the mean location of each cluster. Next, the FCM algorithm sets a membership degree for each data point at each cluster, and then iteratively moves the cluster centers *cj*

> 

*ji*

1

*m*

1 2

*cx cx*

 

1

*ij*

*=u*

*<sup>C</sup>*

*=k ki*

*=i*

and updates the membership degrees *uij*:

*m <sup>m</sup> ij cxu=J* 1 1

*ji*

2

2/ exp

*ji*

*r ca*

 

2

2

$$\mathcal{C}\_j = \frac{\sum\_{i=1}^N \boldsymbol{\mu}\_{\boldsymbol{\mathcal{G}}}^m \cdot \boldsymbol{\mathcal{X}}\_i}{\sum\_{i=1}^N \boldsymbol{\mu}\_{\boldsymbol{\mathcal{G}}}^m}$$

This iteration process will continue till |U(k+1)-U(k)|<ε, where ε is a termination criterion between 0 and 1, U is [uij] matrix and k is the number of iterations.

In should be noted that the structure of fuzzy inference systems is based on Sugeno (or Takagi-Sugeno-Kang) model [Sugeno & Takagi, 1985]. This model is computationally more efficient and thus gives a faster response, where quick decisions should be taken.

For better description, a typical fuzzy inference system on the basis of FCM clustering algorithm was built as example using the data of one chosen patient from table one with Right Lower Lung (RLL) cancer. Figure 3-a shows a set of Gaussian membership functions generated by this fuzzy inference system on input data given by three external markers that move on three X, Y and Z directions (totally 9 inputs) and figure 3-b illustrates the same membership functions using the same algorithm on output data given by implanted internal marker only on X direction. In this inference system three clusters and hence three *if-then* rules connected with AND operator, have been utilized.

(a)

(b) Fig. 3. Gaussian Membership functions generated by fuzzy inference system on the basis of FCM clustering algorithm using total 9 inputs dataset (panels a) and one output dataset

(panel b)

Fig. 3. Gaussian Membership functions generated by fuzzy inference system on the basis of FCM clustering algorithm using total 9 inputs dataset (panels a) and one output dataset (panel b)

A Clinical Application of Fuzzy Logic 13

example. As shown, the lowest square represents the accumulation of all available truncated

Fig. 6. Accumulation of all truncated fuzzy sets in aggregation step

was obtained by Centroid Calculation method.

estimated in real-time condition.

*Defuzzification*: This step acts as final step and the input is aggregated fuzzy set where the output is a single number that returns the center of the cumulated area under the curve. Defuzzification is performed using five built-in methods. In our example the single output

For real-time tumor tracking the correlation models should be executed without a significant delay such that on-time compensation strategy can be applied against tumor motion. Therefore, the execute time of each correlation model that strongly depends on the utilized mathematical procedures, should be taken into account for clinical application. The features of fuzzy model make it very quick in execution, such that the tumor position can be

As final part of this chapter, in order to visualize the performance of fuzzy model in tumor motion tracking, one patient database was selected for model configuration and operation. The chosen patient has Right Lower Lung (RLL) cancer belonging to control group. The number of training dataset used for model configuration in pre-treatment step for this case is 11. Figure 7 shows the tumor motion tracking of this case (red line) versus Cyberknife modeler (blue line) over 5 minutes of treatment time on X, Y and Z directions. The imaging points indicated by green squares in these figures were taken by stereoscopic X-ray imaging system and represent the exact position of tumor motion at that time. As mentioned in this chapter, these points are used for model performance assessment and also model updating during the treatment. As shown, there are five green square points on each panel that

indicates the updating process has been done every one minute for this case.

fuzzy sets.

#### **3. Operation of fuzzy correlation model**

When a fuzzy model was built by training dataset, each external marker data is applied as input and the following steps are accomplished by fuzzy model to estimate the tumor motion as output.

*Fuzzification*: This step takes the inputs and determine their participate degrees at each cluster via generated membership functions (similar to membership function visualized in the previous section).

*Applying AND/OR operator*: When the inputs were fuzzified, if the antecedent of a given rule has more than one part, the fuzzy operator is applied to obtain one number that represents the result of antecedent for that rule. In our typical example, three rules were used connected with AND operator. Figure 4 represents the contribution of each input membership function (filled by yellow) and one output membership functions (filled by blue) associated with applied input value.

Fig. 4. Three rules connected with AND operator in antecedent (yellow) and consequent (blue) parts of FIS

*Applying implication*: Implication step in consequent part of FIS uses a single number given by the antecedent part, and the output is a truncated fuzzy set. In the other word, the consequent is reshaped using a function associated with antecedent. The implication step should be applied for each rule. In figure 5, the truncated output fuzzy set was shown by blue color for second rule of our FIS example. As shown in this example, the build-in function of implication step is on the basis of AND (*minimum selection criteria*) operation.

Fig. 5. Truncated output fuzzy set visualized by blue as result of implication step based on AND operation

*Applying aggregation*: This step receives all the truncated output fuzzy set of each rule and cumulate them as one fuzzy set. Figure 6 shows the aggregation step applied of our

When a fuzzy model was built by training dataset, each external marker data is applied as input and the following steps are accomplished by fuzzy model to estimate the tumor

*Fuzzification*: This step takes the inputs and determine their participate degrees at each cluster via generated membership functions (similar to membership function visualized in

*Applying AND/OR operator*: When the inputs were fuzzified, if the antecedent of a given rule has more than one part, the fuzzy operator is applied to obtain one number that represents the result of antecedent for that rule. In our typical example, three rules were used connected with AND operator. Figure 4 represents the contribution of each input membership function (filled by yellow) and one output membership functions (filled by

Fig. 4. Three rules connected with AND operator in antecedent (yellow) and consequent

*Applying implication*: Implication step in consequent part of FIS uses a single number given by the antecedent part, and the output is a truncated fuzzy set. In the other word, the consequent is reshaped using a function associated with antecedent. The implication step should be applied for each rule. In figure 5, the truncated output fuzzy set was shown by blue color for second rule of our FIS example. As shown in this example, the build-in function of implication step is on the basis of AND (*minimum selection criteria*) operation.

Fig. 5. Truncated output fuzzy set visualized by blue as result of implication step based on

*Applying aggregation*: This step receives all the truncated output fuzzy set of each rule and cumulate them as one fuzzy set. Figure 6 shows the aggregation step applied of our

**3. Operation of fuzzy correlation model** 

blue) associated with applied input value.

motion as output.

the previous section).

(blue) parts of FIS

AND operation

example. As shown, the lowest square represents the accumulation of all available truncated fuzzy sets.

Fig. 6. Accumulation of all truncated fuzzy sets in aggregation step

*Defuzzification*: This step acts as final step and the input is aggregated fuzzy set where the output is a single number that returns the center of the cumulated area under the curve. Defuzzification is performed using five built-in methods. In our example the single output was obtained by Centroid Calculation method.

For real-time tumor tracking the correlation models should be executed without a significant delay such that on-time compensation strategy can be applied against tumor motion. Therefore, the execute time of each correlation model that strongly depends on the utilized mathematical procedures, should be taken into account for clinical application. The features of fuzzy model make it very quick in execution, such that the tumor position can be estimated in real-time condition.

As final part of this chapter, in order to visualize the performance of fuzzy model in tumor motion tracking, one patient database was selected for model configuration and operation. The chosen patient has Right Lower Lung (RLL) cancer belonging to control group. The number of training dataset used for model configuration in pre-treatment step for this case is 11. Figure 7 shows the tumor motion tracking of this case (red line) versus Cyberknife modeler (blue line) over 5 minutes of treatment time on X, Y and Z directions. The imaging points indicated by green squares in these figures were taken by stereoscopic X-ray imaging system and represent the exact position of tumor motion at that time. As mentioned in this chapter, these points are used for model performance assessment and also model updating during the treatment. As shown, there are five green square points on each panel that indicates the updating process has been done every one minute for this case.

A Clinical Application of Fuzzy Logic 15

As depicted in figure 7, the performance of fuzzy correlation model in tumor tracking is comparable with Cyberknife modeler, although a negligible local noise is observed around the inhalation/exhalation peaks. In some peaks there are also some over estimation with respect to Cyberknife modeler performance that is highly visible in the last peak shown in

Moreover, two alternative correlation models were taken into account based on artificial

3D targeting error was calculated for control and worst cases applying fuzzy, ANNs and state models, by means of all imaging points in a same condition [Torshabi et al., 2010]. In this calculation imaging points were utilized as reference points in order to investigate the model performance accuracy. For this aim, the distance between predicted point as given output of three correlation models and corresponding imaging point is measured as model accuracy criteria .Where the assumed predicted point was close to the corresponding imaging point, that model acts reasonably. In contrast, when the predicted point is far away from the corresponding imaging point the accuracy of model performance is missing.

As resulted from this comparative assessment, it can be noted that for control cases where the tracking errors are in a normal interval, there is a good agreement between the performance of three modelers versus Cyberknife. In contrast, for worst cases the fuzzy model has the best performance even better than Cyberknife modeler. In this comparison state model acts as worst prediction model. In worst cases an error reduction improvement was resulted from fuzzy model with respect to Cyberknife that is 10.8% at the 95% confidence level. More detailed information concerning the structure and operation of state

In this chapter a clinical application of fuzzy logic was taken into account for cancer treatment by developing a fuzzy correlation model. This model act as prediction model and track the moving targets, placed in lung and abdomen regions of patient body. For this aim the internal-external markers data were utilized for fuzzy model generation (pre-treatment), operation & updating (during the treatment). Fuzzy model structure and different steps of model performance were explained graphically for a real case. Finally a comparative investigation was preformed between fuzzy model performance and two different correlation models based on Artificial Neural Network and State model. The analyzed results represents that the fuzzy model performance is the best with less error and negligible executive time among the modelers. In general, fuzzy model features make it robust for modeling some systems that are too complex to be modeled by means of conventional mathematical techniques. The application of the fuzzy logic is also highly recommended whenever the available dataset is not qualitatively perfect or has a large degree of variability. As drawback point, it should be considered that the fuzzy model has some local small noises near the inhalation/exhalation peaks as depicted in figure 7, such that two artificial neural network and state models can track the motion more smoothly with less

In current fuzzy model descibed above, a single output that is tumor motion is properly estimated by means of multi-inputs that is three external markers data. This motion

neural network and State model, as mentioned in Introduction section.

model and ANNs with respect to fuzzy model was given by Torshabi et al.

middle panel of this figure.

**4. Conclusion** 

local ripples.

Fig. 7. Tumor motion tracking over time on X (upper panel), Y (middle panel) and Z (lower panel) directions in fuzzy model versus Cyberknife modeler

Fig. 7. Tumor motion tracking over time on X (upper panel), Y (middle panel) and Z (lower

panel) directions in fuzzy model versus Cyberknife modeler

As depicted in figure 7, the performance of fuzzy correlation model in tumor tracking is comparable with Cyberknife modeler, although a negligible local noise is observed around the inhalation/exhalation peaks. In some peaks there are also some over estimation with respect to Cyberknife modeler performance that is highly visible in the last peak shown in middle panel of this figure.

Moreover, two alternative correlation models were taken into account based on artificial neural network and State model, as mentioned in Introduction section.

3D targeting error was calculated for control and worst cases applying fuzzy, ANNs and state models, by means of all imaging points in a same condition [Torshabi et al., 2010]. In this calculation imaging points were utilized as reference points in order to investigate the model performance accuracy. For this aim, the distance between predicted point as given output of three correlation models and corresponding imaging point is measured as model accuracy criteria .Where the assumed predicted point was close to the corresponding imaging point, that model acts reasonably. In contrast, when the predicted point is far away from the corresponding imaging point the accuracy of model performance is missing.

As resulted from this comparative assessment, it can be noted that for control cases where the tracking errors are in a normal interval, there is a good agreement between the performance of three modelers versus Cyberknife. In contrast, for worst cases the fuzzy model has the best performance even better than Cyberknife modeler. In this comparison state model acts as worst prediction model. In worst cases an error reduction improvement was resulted from fuzzy model with respect to Cyberknife that is 10.8% at the 95% confidence level. More detailed information concerning the structure and operation of state model and ANNs with respect to fuzzy model was given by Torshabi et al.

#### **4. Conclusion**

In this chapter a clinical application of fuzzy logic was taken into account for cancer treatment by developing a fuzzy correlation model. This model act as prediction model and track the moving targets, placed in lung and abdomen regions of patient body. For this aim the internal-external markers data were utilized for fuzzy model generation (pre-treatment), operation & updating (during the treatment). Fuzzy model structure and different steps of model performance were explained graphically for a real case. Finally a comparative investigation was preformed between fuzzy model performance and two different correlation models based on Artificial Neural Network and State model. The analyzed results represents that the fuzzy model performance is the best with less error and negligible executive time among the modelers. In general, fuzzy model features make it robust for modeling some systems that are too complex to be modeled by means of conventional mathematical techniques. The application of the fuzzy logic is also highly recommended whenever the available dataset is not qualitatively perfect or has a large degree of variability. As drawback point, it should be considered that the fuzzy model has some local small noises near the inhalation/exhalation peaks as depicted in figure 7, such that two artificial neural network and state models can track the motion more smoothly with less local ripples.

In current fuzzy model descibed above, a single output that is tumor motion is properly estimated by means of multi-inputs that is three external markers data. This motion

A Clinical Application of Fuzzy Logic 17

Jang, J.; Chuen-Tsai, S. & Mizutani, E. (1997). Neuro fuzzy modeling and soft computing.

Kakar, M.; Nyström, H.; Aarup, L.R; Nøttrup, T.J. & Olsen, D.R. (2005). Respiratory motion

Kang, S.J.; Woo, C.H.; Hwang, H.S. & Woo, K.B. (2000). Evolutionary design of fuzzy rule base for nonlinear system modeling and control. *IEEE Trans. Fuzzy Syst.*, Vol. 8, pp. 37-45 Keall, P.J.; Mageras, G.S.; Balter, J.M.; Emery, R.S.; Forster, K.M.; Jiang, S.B.; Kapatoes, J.M.;

Oncology report of AAPM task group 76. *Med. Phys.,* Vol. 33, pp. 3874-3900 Kubo, H.D. & Hill, B.C. (1996). Respiration gated radiotherapy treatment: A technical study.

Lin, C.K. & Wang, S.D. (1999). Fuzzy system identification using an adaptive learning rule

Minohara, S.; Kanai, T.; Endo, M.; Noda, K. & Kanazawa, M. (2000). Respiratory gated

Murphy, M.J. & Dieterich, S. (2006). Comparative performance of linear and nonlinear neural networks to predict irregular breathing. *Phys. Med. Biol.*, Vol. 51, pp. 5903–5914 Ohara, K.; Okumura, T.; Akisada, M.; Inada, T.; Mori, T.; Yokota, H. & Calaguas, M.J. (1989).

Procházka, A.; Pavelka, A. (2007). Feed-Foward and Recurrent Neural Networks in Signal

Ramrath, L.; Schlaefer, A.; Ernst, F.; Dieterich, S. & Schweikard, A. (2007). Prediction of

Riaz, N.; Shanker, P.; Gudmundsson, O.; Wiersrma, R.; Mao, W.; Widrow, B. & Xing, L.

Ruan, D.; Fessler, J.A; Balter, J.M; Berbeco, R.I.; Nishioka, S. & Shirato, H. (2008). Inference of

Seppenwoolde, Y.; Berbeco, R.I.; Nishioka, S.; Shirato, H. & Heijmen, B. (2007). Accuracy of

Sharp, G.C.; Jiang, S.B.; Shimizu, S. & Shirato, H. (2004). Prediction of respiratory tumour

Shi, Y.; Eberhart, R. & Chen, Y. (1999). Implementation of evolutionary fuzzy systems. *IEEE* 

*Radiology and Surgery (CARS'07)*, Vol. 21, Berlin, Germany, 2007

networks. *Clinical Neurophysiology*, Vol. 113, pp. 694-701

approach. *Phys. Med. Biol.*, Vol. 53, pp. 2923-2936

*Trans. Fuzzy Syst.*, Vol. 7, pp. 109-119

a simulation study. *Med. Phys.*, Vol. 34, pp. 2774-2784

Smith, A. (2006). Proton therapy. Phys. Med. Biol., Vol. 51, pp. 491-504

with terminal attractors *J. Fuzzy Sets Syst.*, Vol. 101, pp. 343-352

prediction by using the adaptive neuro fuzzy inference system (ANFIS) *Phys. Med.* 

Low, D.A.; Murphy, M.J.; Murray, B.R.; Ramsey, C.R.; van Herk, M.B.; Vedam, S.S.; Wong, J.W. & Yorke, E. (2006). The Management of Respiratory Motion in Radiation

irradiation system for heavy-ion radiotherapy. *Int. J. Radiat. Oncol., Biol., Phys.* Vol.

Irradiation synchronized with respiration gate. *Int. J. Radiat. Oncol., Biol., Phys.* Vol.

Prediction. *Proceedings the 5th IEEE Int. Conference on Computational Cybernetics*,

respiratory motion with a multi-frequency based Extended Kalman Filter. *Proceedings of the 21st International Conference and Exhibition on Computer Assisted* 

(2009). Predicting respiratory tumor motion with Multi-dimensional Adaptive Filters and Support Vector Regression. *Phys. Med. Biol.*, Vol. 54, pp. 5735-5718 Robert, C.; Gaudy, J.F. & Limoge, A. (2002). Electroencephalogram processing using neural

hysteretic respiratory tumor motion from external surrogates: a state augmentation

tumor motion compensation algorithm from a robotic respiratory tracking system:

motion for real-time image-guided radiotherapy. *Phys. Med. Biol.*, Vol. 49, pp. 425-440

Prentice-Hall, Englewood Cliffs

*Phys. Med. Biol.* Vol. 41, pp. 83-91

47, pp. 1097-1103

17, pp. 853-857

Gammarth, Tunisia, 2007

*Biol.*, Vol. 50, pp. 4721-4728

prediction is suitable for treating the tumors by resiratory-gated radiotherapy approach which in the beam is irradiating only in a pre-defined gating window. As future work, the prediction of volumetric information of tumor motion will be invstigated that is needed for tumor treatment by Real-Time Tumor Tracking Radiotherapy. In this alternative method of radiotherapy that is still in reasearch step, 2D information of tumor contour motion at each moment of treatment time is required. Therefore, The prediction model must work as multiinput/multi-output model such that the multi-output is some finite pionts located on tumor contour at each tumor slice. By this way 3D information of tumor motion and also its deformation can be estimated during the breathing cycle. But the main open isuues that must be addressed in this proposal are restriction in extracting minimum required points of tumor contours at different tumor slices as multi-input data for model configuration and also low quality of Orthogonal X-ray images for model updating.

#### **5. Acknowledgment**

The authors acknowledge Sonja Dieterich for providing access to the clinical database. The research leading to these results has received funding from the European Community's Seventh Framework Programme ([FP7/2007-2013] under grant agreement n° 215840-2).

#### **6. References**


prediction is suitable for treating the tumors by resiratory-gated radiotherapy approach which in the beam is irradiating only in a pre-defined gating window. As future work, the prediction of volumetric information of tumor motion will be invstigated that is needed for tumor treatment by Real-Time Tumor Tracking Radiotherapy. In this alternative method of radiotherapy that is still in reasearch step, 2D information of tumor contour motion at each moment of treatment time is required. Therefore, The prediction model must work as multiinput/multi-output model such that the multi-output is some finite pionts located on tumor contour at each tumor slice. By this way 3D information of tumor motion and also its deformation can be estimated during the breathing cycle. But the main open isuues that must be addressed in this proposal are restriction in extracting minimum required points of tumor contours at different tumor slices as multi-input data for model configuration and

The authors acknowledge Sonja Dieterich for providing access to the clinical database. The research leading to these results has received funding from the European Community's Seventh Framework Programme ([FP7/2007-2013] under grant agreement n° 215840-2).

Azuaje, F.; Dubitzky, W.; Black, N. & Adamson, K. (2000) "Discovering Relevance

Balter, J.M. and Kessler, M.L. (2007). Imaging and alignment for image-guided radiation

Bezdek, J.C. (1981). Pattern Recognition with Fuzzy Objective Function Algoritms. Plenum

Bezdek, J.C.; Pal, N.R. (1998). Some new indexes of cluster validity. *IEEE Trans. Syst. Man.* 

Brown, W.T.; Wu, X.; Fayad, F., Fowler, J.F., Amendola, B.E.; García, S., Han, H.; de la

Chiu, S. (1994). Fuzzy Model Identification Based on Cluster Estimation. *J. Intell. Fuzzy. Syst.*

Dieterich, S.; Cleary, K.; D'Souza, W.; Murphy, M.; Wong, K.H. & Keall, P. (2008). Locating and targeting moving tumors with radiation beams. *Med. Phys.,* Vol. 35, pp. 5684-5694 Dunn, J.C. (1973). A Fuzzy Relative of the ISODATA Process and Its Use in Detecting Compact Well-Separated Clusters. *Journal of Cybernetics*, Vol. 3, pp. 32-57 Evans P.M. (2008). Anatomical imaging for radiotherapy. *Phys. Med. Biol.*, Vol. 53, pp. 151-191 Hoogeman, M.; Prevost, J.B.; Nuyttens, J.; Poll, J.; Levendag, P. & Heumen, B. (2009).

assessment by analysis of log files. *Radiation Oncology*, Vol. 74, pp. 297-303 Jain, A.K.; Murty, M.N. & Flynn, P.J. (1999). Data clustering: a review. *ACM Computing* 

Zerda, A.; Bossart, E.; Huang, Z. & Schwade, J.G. (2007). CyberKnife radiosurgery for stage I lung cancer: results at 36 months, *Clin. Lung Cancer.* Vol. 8, pp. 488-492 Cassileth, B.R. and Deng G. (2004). Complementary and alternative therapies for cancer.

Clinical accuracy of the respiratory tumor tracking system of the cyberknife:

Knowledge in Data: A Growing Cell Structures Approach," *IEEE Trans. Systs. Man.* 

also low quality of Orthogonal X-ray images for model updating.

*Cybern. B Cybern.,* Vol. 30, pp. 448-460

Press, New York, USA

*Cybern.,* Vol. 23, pp. 301-315

*Oncologist.* Vol. 9, pp. 80-89

*Surveys (CSUR).*, Vol. 31, pp. 264-323

Vol. 2, pp. 267-278

therapy. *J. Clin. Oncol*., Vol. 25, pp. 931-937

**5. Acknowledgment** 

**6. References** 


**2** 

 **A Fuzzy Logic Approach for Remote** 

Hamid Medjahed1, Dan Istrate1, Jérôme Boudy2, Jean Louis Baldinger2, Lamine Bougueroua1,

> *1ESIGETEL-LRIT, Avon, 2Telecom SudParis, Evry,*

> > *France*

Mohamed Achraf Dhouib1 and Bernadette Dorizzi2

**Healthcare Monitoring by Learning and** 

**Recognizing Human Activities of Daily Living** 

Improvement of life quality in the developed nations has systematically generated an increase in the life expectancy. A statistic studies curried out by the French national institute of statistic and economic studies (INSEE) shows a new distribution of age classes in France. In fact, almost one in three people will be over 60 years in 2050, against one in five in 2005, and France will have over 10 million of people over 75 years and over 4 million of people over 85 years. Nevertheless, the increasing number of elderly person implies more resources for aftercare, paramedical care and natural assistance in their habitats. The current healthcare infrastructure in those countries is widely considered to be inadequate to meet the needs of this increasingly older population. In this case a permanent assistance is necessary wherever they are, healthcare monitoring is a solution to deal with this problem and ensure the elderly to live safely and independently in their own home for as long as

In order to improve the quality of life of elderly, researchers are developing technologies to enhance a resident's safety and monitor health conditions using sensors and other devices. Numerous projects are carried out in the world especially in Europe, Asia and North America on the home healthcare telemonitoring topic. They aim for example to define a generic architecture for such telemonitoring systems (Doermann et al., 1998), to conduct experiment of a remote monitoring system on a specific category of patients, like people with insufficient cardiac heart, asthma, diabets, patients with Alzheimer's disease, or cognitive impairments (Noury et al., 2003)., or to build smart apartments (Elger et al., 1998), sensors and alarm systems adapted to the healthcare telemonitoring requirements (West et al., 2005). The project CompanionAble is an Integration Project founded by European commission (FP7). In this project we propose a multimodal platform for recognizing human activities of daily living (ADLs) in the home environment, by using a set of sensors in order to provide proactive healthcare telemonitoring for elderly people at home. This platform uses a fuzzy logic approach to fuse three main subsystems, which have been technically

**1. Introduction** 

possible.


### **A Fuzzy Logic Approach for Remote Healthcare Monitoring by Learning and Recognizing Human Activities of Daily Living**

Hamid Medjahed1, Dan Istrate1, Jérôme Boudy2, Jean Louis Baldinger2, Lamine Bougueroua1, Mohamed Achraf Dhouib1 and Bernadette Dorizzi2 *1ESIGETEL-LRIT, Avon, 2Telecom SudParis, Evry, France* 

#### **1. Introduction**

18 Fuzzy Logic – Emerging Technologies and Applications

Su, M.; Miften, M.; Whiddon, C.; Sun, X.; Light, K. & Marks, L. (2005). An artificial neural

Takagi, T. & Sugeno, M. (1985). Fuzzy identification of systems and its application to modeling and control. *IEEE Trans. Syst. Man. Cybern.*, Vol. 15, pp. 116-132 Torshabi, A.E.; Pella, A.; Riboldi, M. & Baroni, G. (2010). Targeting accuracy in real time

Vedam, S.S.; Keall, P.J.; Docef, A.; Todor, D.A.; Kini, V.R. & Mohan, R. (2004). Predicting

Vickers, A. (2004). Alternative cancer cures: 'unproven' or 'disproven'? *CA. Cancer J. Clin.*

Yu, J.; Cheng. Q.; Huang, H. (2004). Analysis of the weighting exponent in the FCM. *IEEE* 

Zadeh, L.A. (1973). Outline of a New Approach to the Analysis of Complex Systems and Decision Processes. *IEEE Trans. Systems, Man and Cybernetics.*, Vol. 3, pp. 28-44

Zadeh, L.A. (1989). Knowledge representation in fuzzy logic. *IEEE Trans. Knowl. Data* 

pp. 318-325

2274–2283

Vol. 9, pp. 551-562

Vol. 54, pp. 110-118

*Eng.*,Vol. 1, pp. 89-100.

*Trans. Syst. Man. Cybern.* Vol. 34, pp. 634-639

Zadeh, L.A. (1988). Fuzzy Logic. *Computer*, Vol. 1, pp. 83-93

Zadeh, L.A. (1965). Fuzzy Sets. *Information and Control*, Vol. 8, pp. 338-353 Zadeh, L.A. (1968). Fuzzy algorithms. *Information and Control*, Vol. 12, pp. 94-102

network for predicting the incidence of radiation pneumonitis. *Med. Phys.*, Vol. 32,

tumor tracking via external sorrugates; a comparative study. *Tech. Canc. Res. Treat.*,

respiratory motion for four-dimensional radiotherapy. *Med. Phys.*, Vol. 31, pp.

Improvement of life quality in the developed nations has systematically generated an increase in the life expectancy. A statistic studies curried out by the French national institute of statistic and economic studies (INSEE) shows a new distribution of age classes in France. In fact, almost one in three people will be over 60 years in 2050, against one in five in 2005, and France will have over 10 million of people over 75 years and over 4 million of people over 85 years. Nevertheless, the increasing number of elderly person implies more resources for aftercare, paramedical care and natural assistance in their habitats. The current healthcare infrastructure in those countries is widely considered to be inadequate to meet the needs of this increasingly older population. In this case a permanent assistance is necessary wherever they are, healthcare monitoring is a solution to deal with this problem and ensure the elderly to live safely and independently in their own home for as long as possible.

In order to improve the quality of life of elderly, researchers are developing technologies to enhance a resident's safety and monitor health conditions using sensors and other devices. Numerous projects are carried out in the world especially in Europe, Asia and North America on the home healthcare telemonitoring topic. They aim for example to define a generic architecture for such telemonitoring systems (Doermann et al., 1998), to conduct experiment of a remote monitoring system on a specific category of patients, like people with insufficient cardiac heart, asthma, diabets, patients with Alzheimer's disease, or cognitive impairments (Noury et al., 2003)., or to build smart apartments (Elger et al., 1998), sensors and alarm systems adapted to the healthcare telemonitoring requirements (West et al., 2005). The project CompanionAble is an Integration Project founded by European commission (FP7). In this project we propose a multimodal platform for recognizing human activities of daily living (ADLs) in the home environment, by using a set of sensors in order to provide proactive healthcare telemonitoring for elderly people at home. This platform uses a fuzzy logic approach to fuse three main subsystems, which have been technically

A Fuzzy Logic Approach for Remote Healthcare

statistical modeling of classes.

sets that reflect activities of daily living.

**3.2 Fuzzy logic and patterns recognition systems** 

maximal granularity, i.e. the minimal accuracy.

from a global point of view:

done mainly at two levels:

**3.1 Data fusion** 

Monitoring by Learning and Recognizing Human Activities of Daily Living 21

In order to maximize a correct recognition of the various ADLs like sleeping, cleaning, bathing etc..., data fusion over the different sensors types is studied. The area of data fusion has generated great interest among researchers in several science disciplines and

 Those that are based on probabilistic models such as Bayesian reasoning (Cowell et al., 1999) and the geometric decision reasoning like Mahalanobis distance, but their performances are limited when the data are heterogeneous and insufficient for a correct

 Those based on connectionist models such as neural networks MLP (Dreyfus et al., 2002) and SVM (Burges et al., 1998) which are very powerful because they can model

Based on those facts the use of fuzzy logic in our platform is motivated by two main raisons

 Firstly the characteristic of data to merge which are measurements obtained from different sensors, thus they could be imprecise and imperfect. Plus the lack of training

 Secondly, Fuzzy logic can gather performance and intelligibility and it deals with imprecision and uncertainty. Its history proves that it is used in many cases which are necessary for pattern recognition applications. It has a background application history to clinical problems including use in automated diagnosis (Adlassnig et al., 1986), control systems (Mason et al., 1997), image processing (Lalande et al., 1997) and pattern recognition (Zahlmann et al., 1997). For medical experts it is easier to map their knowledge onto fuzzy relationships than to manipulate complex probabilistic tools.

Fuzzy logic is a fuzzy set theory, introduced by Lotfi A. Zadeh (Zadeh, 1978) in 1965; it is an extension of classical set theory. Historically, this was closely related to the concept of fuzzy measure, proposed just after by Sugeno (Sugeno, 1974). Similar attempts at proposing fuzzy concept were also made at the same time by Shafer (evidence theory (Shafer, 1974)) and Shackle (surprise theory (Shackle, 1961)). Since that time, fuzzy logic has been more studied, and several applications were developed, essentially in Japan. The use of fuzzy sets can be

 **Attributes representation:** It may happen that data are uncompleted or noisy, unreliable, or some attributes are difficult to measure accurately or difficult to quantify numerically. At that time, it is natural to use fuzzy sets to describe the value of these parameters. The attributes are linguistic variables, whose values are built with adjectives and adverbs of language: large, small, medium etc...and as an illustrating example, we found the recognition system proposed by Mandal et al. (Mandal et al.,1992). Some methods are based on a discretization of the attributes space defined as language. Thus a numerical scale of length will be replaced by a set of fuzzy labels, for example (very small, small, medium, large, extra large), and any measure of length, even numerical is converted on this scale. The underlying idea is to work with the

engineering domains. We have identified two major classes of fusion techniques:

the strong nonlinearity of data but with complex architecture.

validated from end to end, through their hardware and software. The first subsystem is Anason (Rougui et al., 2009) with its set of microphones that allow sound remote monitoring of the acoustical environment of the elderly. The second subsystem is RFpat (Medjahed et al., 2008), a wearable device fixed on the elderly person, which can measure physiological data (cardiac frequency, activity or agitation, posture and fall detection sensor). The last subsystem is a set of infrared sensors and domotic sensors like contact sensors, temperature sensors, smoke sensors and several other domotic sensors for environment conditions monitoring (Medjahed et al., 2008). This fuzzy logic approach allowed us to recognize several activities of daily living (ADLs) for ubiquitous healthcare. The decision of this multimodal data fusion platform is sent to a remote monitoring center to take action in the case of distress situation.

#### **2. CompanionAble project**

The CompanionAble project aim to provide the synergy of Robotics and Ambient Intelligence technologies and their semantic integration to provide for a care-giver's assistive environment. This will support the cognitive stimulation and therapy management of the care-recipient. This is mediated by a robotic companion (mobile facilitation) working collaboratively with a smart home environment (stationary facilitation).

There are widely acknowledged imperatives for helping the elderly live at home (semi) independently for as long as possible. Without cognitive stimulation support the elderly dementia and depression sufferers can deteriorate rapidly and the carers will face a more demanding task. Both groups are increasingly at the risk of social exclusion.

The distinguishing advantages of the CompanionAble Framework Architecture arise from the objective of graceful, scalable and cost-effective integration. Thus CompanionAble addresses the issues of social inclusion and homecare of persons suffering from chronic cognitive disabilities prevalent among the increasing European older population. A participative and inclusive co-design and scenario validation approach will drive the RTD efforts in CompanionAble; involving care recipients and their close carers as well as the wider stakeholders. This is to ensure end-to-end systemic viability, flexibility, modularity and affordability as well as a focus on overall care support governance and integration with quality of experience issues such as dignity-privacy-security preserving responsibilities fully considered.

CompanionAble will be evaluated at a number of testbeds representing a diverse European user-base as the proving ground for its socio-technical-ethical validation. The collaboration of leading gerontologists, specialist elderly care institutions, industrial and academic RTD partners, including a strong cognitive robotics and smart-house capability makes for an excellent confluence of expertise for this innovative project.3. State of the art

Everyday life activities in the home split into two categories. Some activities show the motion of the human body and its structure. Examples are walking, running, standing up, setting down, laying and exercising. These activities may be mostly recognized by using sensors that are placed on the body (Lee et al., 2002). A second class of activities is recognized by identifying or looking for patterns in how people move things. In this work we focus on some activities identification belong to these both categories.

#### **3.1 Data fusion**

20 Fuzzy Logic – Emerging Technologies and Applications

validated from end to end, through their hardware and software. The first subsystem is Anason (Rougui et al., 2009) with its set of microphones that allow sound remote monitoring of the acoustical environment of the elderly. The second subsystem is RFpat (Medjahed et al., 2008), a wearable device fixed on the elderly person, which can measure physiological data (cardiac frequency, activity or agitation, posture and fall detection sensor). The last subsystem is a set of infrared sensors and domotic sensors like contact sensors, temperature sensors, smoke sensors and several other domotic sensors for environment conditions monitoring (Medjahed et al., 2008). This fuzzy logic approach allowed us to recognize several activities of daily living (ADLs) for ubiquitous healthcare. The decision of this multimodal data fusion platform is sent to a remote monitoring center

The CompanionAble project aim to provide the synergy of Robotics and Ambient Intelligence technologies and their semantic integration to provide for a care-giver's assistive environment. This will support the cognitive stimulation and therapy management of the care-recipient. This is mediated by a robotic companion (mobile facilitation) working

There are widely acknowledged imperatives for helping the elderly live at home (semi) independently for as long as possible. Without cognitive stimulation support the elderly dementia and depression sufferers can deteriorate rapidly and the carers will face a more

The distinguishing advantages of the CompanionAble Framework Architecture arise from the objective of graceful, scalable and cost-effective integration. Thus CompanionAble addresses the issues of social inclusion and homecare of persons suffering from chronic cognitive disabilities prevalent among the increasing European older population. A participative and inclusive co-design and scenario validation approach will drive the RTD efforts in CompanionAble; involving care recipients and their close carers as well as the wider stakeholders. This is to ensure end-to-end systemic viability, flexibility, modularity and affordability as well as a focus on overall care support governance and integration with quality of experience issues such as dignity-privacy-security preserving responsibilities fully

CompanionAble will be evaluated at a number of testbeds representing a diverse European user-base as the proving ground for its socio-technical-ethical validation. The collaboration of leading gerontologists, specialist elderly care institutions, industrial and academic RTD partners, including a strong cognitive robotics and smart-house capability makes for an

Everyday life activities in the home split into two categories. Some activities show the motion of the human body and its structure. Examples are walking, running, standing up, setting down, laying and exercising. These activities may be mostly recognized by using sensors that are placed on the body (Lee et al., 2002). A second class of activities is recognized by identifying or looking for patterns in how people move things. In this work

collaboratively with a smart home environment (stationary facilitation).

demanding task. Both groups are increasingly at the risk of social exclusion.

excellent confluence of expertise for this innovative project.3. State of the art

we focus on some activities identification belong to these both categories.

to take action in the case of distress situation.

**2. CompanionAble project** 

considered.

In order to maximize a correct recognition of the various ADLs like sleeping, cleaning, bathing etc..., data fusion over the different sensors types is studied. The area of data fusion has generated great interest among researchers in several science disciplines and engineering domains. We have identified two major classes of fusion techniques:


Based on those facts the use of fuzzy logic in our platform is motivated by two main raisons from a global point of view:


#### **3.2 Fuzzy logic and patterns recognition systems**

Fuzzy logic is a fuzzy set theory, introduced by Lotfi A. Zadeh (Zadeh, 1978) in 1965; it is an extension of classical set theory. Historically, this was closely related to the concept of fuzzy measure, proposed just after by Sugeno (Sugeno, 1974). Similar attempts at proposing fuzzy concept were also made at the same time by Shafer (evidence theory (Shafer, 1974)) and Shackle (surprise theory (Shackle, 1961)). Since that time, fuzzy logic has been more studied, and several applications were developed, essentially in Japan. The use of fuzzy sets can be done mainly at two levels:

 **Attributes representation:** It may happen that data are uncompleted or noisy, unreliable, or some attributes are difficult to measure accurately or difficult to quantify numerically. At that time, it is natural to use fuzzy sets to describe the value of these parameters. The attributes are linguistic variables, whose values are built with adjectives and adverbs of language: large, small, medium etc...and as an illustrating example, we found the recognition system proposed by Mandal et al. (Mandal et al.,1992). Some methods are based on a discretization of the attributes space defined as language. Thus a numerical scale of length will be replaced by a set of fuzzy labels, for example (very small, small, medium, large, extra large), and any measure of length, even numerical is converted on this scale. The underlying idea is to work with the maximal granularity, i.e. the minimal accuracy.

A Fuzzy Logic Approach for Remote Healthcare

could take only two values: () 1 *<sup>A</sup>*

Fig. 1. Fuzzy inference system steps.

straight lines can formally be defined as follows:

Trapezoidal function furnished in the equation (3).

width of the function is defined by:

inference system steps.

**3.3.1 Fuzzification** 

speak about the truth value.

Where ( ) *<sup>A</sup>* 

Monitoring by Learning and Recognizing Human Activities of Daily Living 23

to classical logic where the membership function \_A(x) of an element x belonging to a set *A*

A typical fuzzy logic inference system has four components: the fuzzification, the fuzzy rule base plus the inference engine, and the defuzzification. Figure 1 shows those main fuzzy

First step in fuzzy logic is to convert the measured data into a set of fuzzy variables. It is done by giving value (these will be our variables) to each of a membership functions set. Membership functions take different shape. A Triangular membership function with

0,

 

*x a*

*x c*

*x a*

*x d*

 

*x a b aa x b*

( ) /( ),

*x a b aa x b*

*d x d cc x d*

( ) /( ),

*c x c bb x c*

( ) /( ), (,,,) ( ) /( ),

*xabc*

( , , , , ) 1,

A Gaussian membership function with the parameters m and

*f xabcd b x c*

0,

0,

0,

*x* if *x A* or

the concept of membership degree of an element *x* to a set *A* and ( ) [0;1] *<sup>A</sup>*

*x* in equation (1), is the membership function (MF) of each *x* in *A* . In contrast

A(x) 0 if *x A* , fuzzy logic introduces

*x* , here we

(2)

(3)

to control the center and

 **Class representation:** Groups do not create a clear partition of the data space, but a fuzzy partition where recovery is allowed will be better adapted. A significant number of fuzzy patterns recognition methods, are just an extension of traditional methods based on the idea of fuzzy partition for example the fuzzy c-means algorithm (Pedrycz, 1990). Historically, the idea of fuzzy partition was first proposed by Ruspini in 1969 (Ruspini, 1969).

Rather than creating new methods of fusion and patterns recognition based on entirely different approaches, fuzzy logic fits naturally in the expression of the problem of classification, and tend to make a generalization of the classification methods that already exist. Taking into account the four steps of a recognition system proposed by Bezdek et Pal (Bezdek et al., 1992), fuzzy logic is very useful for these steps.


#### **3.3 Fuzzy logic steps**

We concentrate our efforts in emphasizing the fuzzy logic concept in order to integrate this fundamental approach within the telemonitoring platform. The main concept of fuzzy logic is that many problems in the real world are imprecise rather than exact (Buckley et al., 2002). It is believed that the effectiveness of the human brain is not only from precise cognition, but also from fuzzy concepts, fuzzy judgment, and fuzzy reasoning. An advantage of fuzzy classification techniques lies in the fact that they provide a soft decision, a value that describes the degree to which a pattern fits within a class, rather than only a hard decision, i.e., a pattern matches a class or not. Fuzzy logic is based on natural language which makes it quite attracting field in artificial intelligence. It allows the natural description of problem domains, in linguistic terms, rather than in terms of relationships between precise numerical values.

A fuzzy set, as the foundation of fuzzy logic, is a set without a hard, clearly sharp defined boundary. A fuzzy set extends a standard set by allowing degrees of membership of an element to this set, measured by real numbers in the [0;1] interval. If *X* is the universe of discourse (the input space variable) and its elements are denoted by *x* , then a fuzzy set *A* on *X* is defined as a set of ordered pairs ( , ( )) *<sup>A</sup> x x* such that:

$$A = \{ \mathbf{x}, \mu\_A(\mathbf{x}) \mid \mathbf{x}, 0 \le \mu\_A(\mathbf{x}) \le 1 \quad \} \tag{1}$$

Where ( ) *<sup>A</sup> x* in equation (1), is the membership function (MF) of each *x* in *A* . In contrast to classical logic where the membership function \_A(x) of an element x belonging to a set *A* could take only two values: () 1 *<sup>A</sup> x* if *x A* or A(x) 0 if *x A* , fuzzy logic introduces the concept of membership degree of an element *x* to a set *A* and ( ) [0;1] *<sup>A</sup> x* , here we speak about the truth value.

Fig. 1. Fuzzy inference system steps.

A typical fuzzy logic inference system has four components: the fuzzification, the fuzzy rule base plus the inference engine, and the defuzzification. Figure 1 shows those main fuzzy inference system steps.

#### **3.3.1 Fuzzification**

22 Fuzzy Logic – Emerging Technologies and Applications

 **Class representation:** Groups do not create a clear partition of the data space, but a fuzzy partition where recovery is allowed will be better adapted. A significant number of fuzzy patterns recognition methods, are just an extension of traditional methods based on the idea of fuzzy partition for example the fuzzy c-means algorithm (Pedrycz, 1990). Historically, the idea of fuzzy partition was first proposed by Ruspini in 1969

Rather than creating new methods of fusion and patterns recognition based on entirely different approaches, fuzzy logic fits naturally in the expression of the problem of classification, and tend to make a generalization of the classification methods that already exist. Taking into account the four steps of a recognition system proposed by Bezdek et Pal

 **Data description:** Fuzzy logic is used to describe syntactic data (Mizumoto et al., 1972), numerical and contextual data, conceptual or rules based data (Pao et al., 1989) which is

 **Analysis of discriminate parameters:** In image processing, there are many techniques based on fuzzy logic for segmentation, detection, contrast enhancement (Keller et al

 **Clustering algorithms:** The aim of these algorithms is to label a set of data into C groups, so that obtained groups contain the most possible similar individuals. Fuzzy cmean algorithm and fuzzy ISODATA (Dunn, 1973) algorithm are the better known in

 **Design of the discriminator:** The discriminator is designed to produce a fuzzy partition or a clear one, describing the data. This partition corresponds to a set of classes. Indeed

We concentrate our efforts in emphasizing the fuzzy logic concept in order to integrate this fundamental approach within the telemonitoring platform. The main concept of fuzzy logic is that many problems in the real world are imprecise rather than exact (Buckley et al., 2002). It is believed that the effectiveness of the human brain is not only from precise cognition, but also from fuzzy concepts, fuzzy judgment, and fuzzy reasoning. An advantage of fuzzy classification techniques lies in the fact that they provide a soft decision, a value that describes the degree to which a pattern fits within a class, rather than only a hard decision, i.e., a pattern matches a class or not. Fuzzy logic is based on natural language which makes it quite attracting field in artificial intelligence. It allows the natural description of problem domains, in linguistic terms, rather than in terms of relationships between precise numerical values.

A fuzzy set, as the foundation of fuzzy logic, is a set without a hard, clearly sharp defined boundary. A fuzzy set extends a standard set by allowing degrees of membership of an element to this set, measured by real numbers in the [0;1] interval. If *X* is the universe of discourse (the input space variable) and its elements are denoted by *x* , then a fuzzy set *A*

, ( )/ ,0 ( ) 1 *A x xx x*

 

such that:

*A A* (1)

(Bezdek et al., 1992), fuzzy logic is very useful for these steps.

1992) and extraction (Pal et al., 1986).

on *X* is defined as a set of ordered pairs ( , ( )) *<sup>A</sup> x x*

the most significant contribution for the data description.

the fuzzy ISODATA algorithm is adapted for this step.

(Ruspini, 1969).

this category.

**3.3 Fuzzy logic steps** 

First step in fuzzy logic is to convert the measured data into a set of fuzzy variables. It is done by giving value (these will be our variables) to each of a membership functions set. Membership functions take different shape. A Triangular membership function with straight lines can formally be defined as follows:

$$\mathsf{A}(\mathsf{x},a,b,c) = \begin{cases} 0, \mathsf{x} \le a \\ (\mathsf{x}-\mathsf{a}) / \,(b-a), a \le \mathsf{x} \le b \\ (c-\mathsf{x}) / \,(c-b), b \le \mathsf{x} \le c \\ 0, \mathsf{x} \ge c \end{cases} \tag{2}$$

Trapezoidal function furnished in the equation (3).

$$f(\mathbf{x}, a, b, c, d) = \begin{cases} 0, \mathbf{x} \le a \\ (\mathbf{x} - a) \ne (b - a), a \le \mathbf{x} \le b \\ 1, b \le \mathbf{x} \le c \\ (d - \mathbf{x}) \ne (d - c), c \le \mathbf{x} \le d \\ 0, \mathbf{x} \ge d \end{cases} \tag{3}$$

A Gaussian membership function with the parameters m and to control the center and width of the function is defined by:

A Fuzzy Logic Approach for Remote Healthcare

Where \*

Monitoring by Learning and Recognizing Human Activities of Daily Living 25

We define a smart environment as one with the ability to adapt the environment to the inhabitants and meet the goals of comfort and efficiency. In order to achieve these goals, our first aim is focused on providing such as environment. We consider our system as an intelligent agent, which perceives the state of the environment using sensors and acts

In-home healthcare devices face a real problem of acceptance by end users and also caregivers. Sound sensors are easily accepted by care receivers and their family, they are considered are less intrusive then cameras, smart T-shirts, etc In order to preserve the carereceiver privacy while ensuring his protection and safety, we propose to equip his house with some microphones. In this context, the sound signal flow is continuously analyzed but not continuously recorded. Among different everyday life sounds, only some of them are considered alarming sounds: glass breaking, screams, etc. In order to have a reliable sound telemonitoring system, every sound event is detected (a sudden change in the environmental noise), extracted, and used as input for the classification stage. The sound

The first module (M.1) is applied to each channel or microphone in order to detect sound events and to extract them from the signal flow. This module use an algorithm based on energy of discrete wavelet transform (DWT) coefficients was proposed and evaluated in (Rougui et al., 2009). This algorithm detects precisely the signal beginning and its end, using

The second module (M.2) is a low-stage classification one. It processes the sound received from the first module (M.1) in order to separate the speech signals from the sound ones. The method used by this module is based on Gaussian Mixture Model (GMM) [14] (K-means followed by Expectation Maximization in 20 steps). There are other possibilities for signal classification: Hidden Markov Model (HMM), Bayesian method, etc. Even if similar results have been obtained with other methods, their high complexity and high time consumption prevent from real-time implementation. A preliminary step before signal classification is the extraction of acoustic parameters: LFCC (Linear Frequency Cepstral Coefficients) 24 filters. The choice of this type of parameters relies on their properties: bank of filters with constant bandwidth, which leads to equal resolution at high frequencies often encountered in life

analysis system has been divided in three modules as shown in Figure 2.

sounds. The best performances have been obtained with 24 Gaussians.

*MOM*

*Z*

( 1,2,...., ) *<sup>i</sup> xi N* reach the maximal values of ( ) *<sup>A</sup>*

**4. The multimodal telemonitoring platform** 

consequently using device controllers.

properties of wavelet transform.

**4.1 Sound environment analysis (Anason)** 

\* 1 *N i i*

> *x*

\* \* min( ) max( ) *Z x and Z x SOM i LOM <sup>i</sup>* (9)

(8)

*x*

*N*

$$\mathbf{G}(\mathbf{x}, m, \sigma) = e^{\frac{-\left(\mathbf{x} - m\right)^2}{2\sigma^2}} \tag{4}$$

The generalized Bell function depends on three parameters a, b, and c is given by:

$$f(\mathbf{x}, a, b, c) = \frac{1}{1 + \left\|(\mathbf{x} - c) / a\right\|^{2b}}\tag{5}$$

There are also other memberships functions like sigmoid shaped function, single function etc... The choice of the function shape is iteratively determined, according to the type of data and taking into account the experimental results.

#### **3.3.2 Fuzzy rules and inference system**

The fuzzy inference system uses fuzzy equivalents of logical AND, OR and NOT operations to build up fuzzy logic rules. An inference engine operates on rules that are structured in an IF-THEN format. The IF part of the rule is called the antecedent, while the THEN part of the rule is called the consequent. Rules are constructed from linguistic variables. These variables take on the fuzzy values or fuzzy terms that are represented as words and modeled as fuzzy subsets of an appropriate domain. There are several types of fuzzy rules, we only mention the two mains used in our system:


#### **3.3.3 Defuzzification**

The last step of a fuzzy logic system consists in turning the fuzzy variables generated by the fuzzy logic rules into real values again which can then be used to perform some action. There are different defuzzification methods; in our platform decision module we could use Centroid Of Area (COA), Bisector Of Area (BOA), Mean Of Maximum (MOM), Smallest Of Maximum (SOM) and Largest Of Maximum (LOM). Equations 6, 7, 8 and 9 illustrate them.

$$Z\_{\rm COA} = \frac{\sum\_{i=1}^{n} \mu\_A(\mathbf{x}\_i)\mathbf{x}\_i}{\sum\_{i=1}^{n} \mu\_A(\mathbf{x}\_i)}\tag{6}$$

$$Z\_{BOA} = \mathbf{x}\_M; \sum\_{i=1}^{M} \mu\_A(\mathbf{x}\_i) = \sum\_{j=M+1}^{n} \mu\_A(\mathbf{x}\_j) \tag{7}$$

$$Z\_{\rm MOM} = \frac{\sum\_{i=1}^{N} \mathbf{x}\_i^\*}{N} \tag{8}$$

$$Z\_{\text{SOM}} = \min(\mathbf{x}\_i^\*) \text{ and } Z\_{\text{LOW}} = \max(\mathbf{x}\_i^\*) \tag{9}$$

Where \* ( 1,2,...., ) *<sup>i</sup> xi N* reach the maximal values of ( ) *<sup>A</sup> x*

#### **4. The multimodal telemonitoring platform**

24 Fuzzy Logic – Emerging Technologies and Applications

<sup>2</sup> (, , )

*Gxm e* 

<sup>1</sup> (,,,) 1 ( )/ *<sup>b</sup> f xabc*

The generalized Bell function depends on three parameters a, b, and c is given by:

and taking into account the experimental results.

many variations by using other operators.

**3.3.2 Fuzzy rules and inference system** 

the two mains used in our system:

outputs.

**3.3.3 Defuzzification** 

2 2 ( )

2

(4)

(5)

*x m*

*xc a*

There are also other memberships functions like sigmoid shaped function, single function etc... The choice of the function shape is iteratively determined, according to the type of data

The fuzzy inference system uses fuzzy equivalents of logical AND, OR and NOT operations to build up fuzzy logic rules. An inference engine operates on rules that are structured in an IF-THEN format. The IF part of the rule is called the antecedent, while the THEN part of the rule is called the consequent. Rules are constructed from linguistic variables. These variables take on the fuzzy values or fuzzy terms that are represented as words and modeled as fuzzy subsets of an appropriate domain. There are several types of fuzzy rules, we only mention

 **Mamdani rules** (Jang et al., 1997) : which are on the form: *If x1 is A1 and x2 is A2 and...and xp is Ap Then y1 is C1 and y2 is C2 and...and yp is Cp* Where *Ai* and *Ci* are fuzzy sets that define the partition space. The conclusion of a Mamdani rule is a fuzzy set. It uses the algebraic product and the maximum as T-norm and S-norm respectively, but there are

 **Takagi/Sugeno rules** (Jang et al., 1997): those rules are on the form : *If x1 is A1 and x2 is A2 and...and xp is Ap Then* y = b 0+b1 x1 +b2 x2 +…+ bp xp. In the Sugeno model the conclusion is numerical. The rules aggregation is in fact the weighted sum of rules

The last step of a fuzzy logic system consists in turning the fuzzy variables generated by the fuzzy logic rules into real values again which can then be used to perform some action. There are different defuzzification methods; in our platform decision module we could use Centroid Of Area (COA), Bisector Of Area (BOA), Mean Of Maximum (MOM), Smallest Of Maximum (SOM) and Largest Of Maximum (LOM). Equations 6, 7, 8 and 9 illustrate them.

> 1 1

  *n*

*COA n*

*Z*

( ) ( )

*x x*

*x*

 

(6)

(7)

*A i i i*

*A i i*

1 1 ; () () *M n BOA M A i A j i j M Zx x x* 

We define a smart environment as one with the ability to adapt the environment to the inhabitants and meet the goals of comfort and efficiency. In order to achieve these goals, our first aim is focused on providing such as environment. We consider our system as an intelligent agent, which perceives the state of the environment using sensors and acts consequently using device controllers.

#### **4.1 Sound environment analysis (Anason)**

In-home healthcare devices face a real problem of acceptance by end users and also caregivers. Sound sensors are easily accepted by care receivers and their family, they are considered are less intrusive then cameras, smart T-shirts, etc In order to preserve the carereceiver privacy while ensuring his protection and safety, we propose to equip his house with some microphones. In this context, the sound signal flow is continuously analyzed but not continuously recorded. Among different everyday life sounds, only some of them are considered alarming sounds: glass breaking, screams, etc. In order to have a reliable sound telemonitoring system, every sound event is detected (a sudden change in the environmental noise), extracted, and used as input for the classification stage. The sound analysis system has been divided in three modules as shown in Figure 2.

The first module (M.1) is applied to each channel or microphone in order to detect sound events and to extract them from the signal flow. This module use an algorithm based on energy of discrete wavelet transform (DWT) coefficients was proposed and evaluated in (Rougui et al., 2009). This algorithm detects precisely the signal beginning and its end, using properties of wavelet transform.

The second module (M.2) is a low-stage classification one. It processes the sound received from the first module (M.1) in order to separate the speech signals from the sound ones. The method used by this module is based on Gaussian Mixture Model (GMM) [14] (K-means followed by Expectation Maximization in 20 steps). There are other possibilities for signal classification: Hidden Markov Model (HMM), Bayesian method, etc. Even if similar results have been obtained with other methods, their high complexity and high time consumption prevent from real-time implementation. A preliminary step before signal classification is the extraction of acoustic parameters: LFCC (Linear Frequency Cepstral Coefficients) 24 filters. The choice of this type of parameters relies on their properties: bank of filters with constant bandwidth, which leads to equal resolution at high frequencies often encountered in life sounds. The best performances have been obtained with 24 Gaussians.

A Fuzzy Logic Approach for Remote Healthcare

Fig. 3. Internal structure of the wearable device (RFpat)

and pushed through this ZigBee link when recovered.

the second being used to supply the analog circuits.

Monitoring by Learning and Recognizing Human Activities of Daily Living 27

In a case of emergency situation, for example if the care receiver has fallen down without standing up, with an eventual short delay, afterwards or has pushed the call button, the wearable device will transmit via ZigBee communication the corresponding alarm index to an in-home base station, which is connected to the multimodal platform. If no emergency event occurs, data are transmitted to this receiver every 30 seconds. In case of wireless link interruption, the data will be stored into an internal flash memory of the ZigBee transceiver

The device use two microcontrollers (Figure 3), the first is processing "actimetric" sensors i.e. fall, movement and tilt sensor and driving analog switches used for the sampling process of the PPG signal pre-conditioner, the second being devoted to the processing of the pulse sensor. The ZigBee transceiver is also driven by the second microcontroller. All the circuits are supplied by a Lithium-Polymer battery element of 3.7 volts followed by 2 voltage regulators providing a voltage of 3 volts, one for the digital circuits and the ZigBee module,

The vital signals terminal is planned as a mobile device worn by the person of care in the smart home environment as well as in the short range outside environment (garden etc.).

Fig. 2. Anason software architecture

The sound classification module (M.3) classifies the detected sound between predefined sound classes. This module is based, also, on a GMM algorithm. The LFCC acoustical parameters have been used for the same reasons than for sound/speech module and with the same composition: 24 filters. A loglikelihood is computed for the unknown signal according to each predefined sound classes; the sound class with the biggest log likelihood is the output of this module.

#### **4.2 Vital signals wearable device (RFpat)**

The wearable device named RFpat (Hoppenot et al., 2009), designed by Telecom SudParis and integrated by ASICA, is devoted to the surveillance of the vital status of the care receiver, transmitting a fall index after validation by an embedded algorithm. Further functionalities of the wearable device include the eventual use of the emergency call button, the determination of the heart pulse rate (beat/minute) and of a posture index, a movement frequency index and a technical status of the device.

The sound classification module (M.3) classifies the detected sound between predefined sound classes. This module is based, also, on a GMM algorithm. The LFCC acoustical parameters have been used for the same reasons than for sound/speech module and with the same composition: 24 filters. A loglikelihood is computed for the unknown signal according to each predefined sound classes; the sound class with the biggest log likelihood

The wearable device named RFpat (Hoppenot et al., 2009), designed by Telecom SudParis and integrated by ASICA, is devoted to the surveillance of the vital status of the care receiver, transmitting a fall index after validation by an embedded algorithm. Further functionalities of the wearable device include the eventual use of the emergency call button, the determination of the heart pulse rate (beat/minute) and of a posture index, a movement

Fig. 2. Anason software architecture

is the output of this module.

**4.2 Vital signals wearable device (RFpat)** 

frequency index and a technical status of the device.

Fig. 3. Internal structure of the wearable device (RFpat)

In a case of emergency situation, for example if the care receiver has fallen down without standing up, with an eventual short delay, afterwards or has pushed the call button, the wearable device will transmit via ZigBee communication the corresponding alarm index to an in-home base station, which is connected to the multimodal platform. If no emergency event occurs, data are transmitted to this receiver every 30 seconds. In case of wireless link interruption, the data will be stored into an internal flash memory of the ZigBee transceiver and pushed through this ZigBee link when recovered.

The device use two microcontrollers (Figure 3), the first is processing "actimetric" sensors i.e. fall, movement and tilt sensor and driving analog switches used for the sampling process of the PPG signal pre-conditioner, the second being devoted to the processing of the pulse sensor. The ZigBee transceiver is also driven by the second microcontroller. All the circuits are supplied by a Lithium-Polymer battery element of 3.7 volts followed by 2 voltage regulators providing a voltage of 3 volts, one for the digital circuits and the ZigBee module, the second being used to supply the analog circuits.

The vital signals terminal is planned as a mobile device worn by the person of care in the smart home environment as well as in the short range outside environment (garden etc.).

A Fuzzy Logic Approach for Remote Healthcare

obtained from each sensor and subsystem.

according to sound sources as it is in table 2.

**Membership Function Composition** 

Speech key words and expressions Multimedia Sounds TV, radio, computer, music Door sounds door clapping, door knob, key ring Water sounds water flushing, water in washbasin,

Table 2. Fuzzy sets defined for the ANASON classification input

levels: low, medium and high.

activity inputs.

getting up, toilet, bathing, going out of home, enter home, washing dishes, doing laundry, washing hands, watching TV, listening radio, cleaning talking on telephone, cooking

Monitoring by Learning and Recognizing Human Activities of Daily Living 29

The first step for developing this approach is the Fuzzification of system outputs and inputs

From Anason subsystem three inputs are built. The first one is the sound environment classification, all detected sound class and expressions are labeled on a numerical scale according to their source. Nine membership functions are set up in this numerical scale

Human Sound snoring, yawn, sneezing, cough, cry, scream,

Ring tone telephone ring, bell door, alarm, alarm clock Object sound chair, table, tear-turn paper, step foot

Machine sounds coffee machine, dishwasher, electrical shaver,

Dishwasher glass vs glass, glass wood, plastic vs plastic,

Two other inputs are associated to each SNR calculated on each microphone (two microphones are used in the current application), and these inputs are split into three fuzzy

The wearable terminal RFpat produce five inputs; Heart rate for which three fuzzy levels are specified normal, low and high; Activity which has four fuzzy sets: immobile, rest, normal and agitation; Posture is represented by two membership functions standing up / sitting

The defined area of each membership function associated to heart rate or activity is adapted to each monitored elderly person. In our application we use only posture, and

down and lying; Fall and call have also two fuzzy levels: Fall/Call and No Fall/Call.

laugh

coffee filter

air conditioner

plastic vs wood, spoon vs table

microwave, vacuum cleaner, washing machine,

sleeping, walking, standing up

setting down, laying

exercising

**ADLs of using devices ADLs of Human body motion** 

Table 1. Fuzzy List ADLS to be recognized by the telemonitoring platform

The mobile device is connected to the base station with a ZigBee network. The simple version of the network is working with two nodes. One node is defined as the coordinator, which is the base station on the central smart home control PC. The other node is defined as one end device, which is normally the wearable device. In poor RF conditions another node defined as a routing device that can extend the range between the base station and the wearable device. We have chosen the ZigBee IEEE 802.15.4 protocol because it is a secure and common protocol in the smart home environment. The most important advantages are the good power management and a good indoor wireless range with added routers if needed, which was preferred to a high bandwidth (WiFi for instance). We normally transmit 3 bytes every 30 seconds.

#### **4.3 Home automation sensors**

The in-home healthcare monitoring systems have to solve an important issue of privacy. When developing our multi-modal platform, we chose the monitoring modules such that they have the less intrusive incidence on the monitored elderly person. We equipped our test apartment with wireless infrared sensors connected to a remote computer. The computer automatically receives and saves data obtained from the different sensors. Data corresponding to movements are collected twice per second, and stored with the event time in a specific file.

The sensors are activated by the person's passage underneath, and remained activated as long as there is movement under that sensor and for an additional time period of ½ seconds after the movement end. The results from the automatic processing of this data are displayed in the form of list with all movements noted together with the time and each movement's duration. This subsystem called Gardien is also able to display the data either in the form of graph (activity duration versus days) or as three-dimensional histograms (each sensor activation versus time).

A set of wireless ambient sensors is added to this subsystem, they are designated for telemonitoring the environment of the patient and his surroundings. It includes state change sensors for active devices detection, contact sensors which are responsible for door and windows opening /closing detection, temperature sensors, fire sensors, flood sensors and light sensors.

#### **5. Fuzzy logic activities recognition approach**

#### **5.1 Parameter and method elaboration**

The main advantages of using fuzzy logic system are the simplicity of the approach and the capacity of dealing with the complex data acquired from the different sensors. Fuzzy set theory offers a convenient way to do all possible combinations with these sensors. Fuzzy set theory is used in this system to monitor and to recognize the activities of people within the environment in order to timely provide support for safety, comfort, and convenience. Automatic health monitoring is predominantly composed of location and activity information. Abnormality also could be indicated by the lack of an activity or an abnormal activity detection which will cause or raise the home anxiety. Table 1 lists what we wish to automatically recognize.

The mobile device is connected to the base station with a ZigBee network. The simple version of the network is working with two nodes. One node is defined as the coordinator, which is the base station on the central smart home control PC. The other node is defined as one end device, which is normally the wearable device. In poor RF conditions another node defined as a routing device that can extend the range between the base station and the wearable device. We have chosen the ZigBee IEEE 802.15.4 protocol because it is a secure and common protocol in the smart home environment. The most important advantages are the good power management and a good indoor wireless range with added routers if needed, which was preferred to a high bandwidth (WiFi for instance). We normally transmit

The in-home healthcare monitoring systems have to solve an important issue of privacy. When developing our multi-modal platform, we chose the monitoring modules such that they have the less intrusive incidence on the monitored elderly person. We equipped our test apartment with wireless infrared sensors connected to a remote computer. The computer automatically receives and saves data obtained from the different sensors. Data corresponding to movements are collected twice per second, and stored with the event time

The sensors are activated by the person's passage underneath, and remained activated as long as there is movement under that sensor and for an additional time period of ½ seconds after the movement end. The results from the automatic processing of this data are displayed in the form of list with all movements noted together with the time and each movement's duration. This subsystem called Gardien is also able to display the data either in the form of graph (activity duration versus days) or as three-dimensional histograms

A set of wireless ambient sensors is added to this subsystem, they are designated for telemonitoring the environment of the patient and his surroundings. It includes state change sensors for active devices detection, contact sensors which are responsible for door and windows opening /closing detection, temperature sensors, fire sensors, flood sensors and

The main advantages of using fuzzy logic system are the simplicity of the approach and the capacity of dealing with the complex data acquired from the different sensors. Fuzzy set theory offers a convenient way to do all possible combinations with these sensors. Fuzzy set theory is used in this system to monitor and to recognize the activities of people within the environment in order to timely provide support for safety, comfort, and convenience. Automatic health monitoring is predominantly composed of location and activity information. Abnormality also could be indicated by the lack of an activity or an abnormal activity detection which will cause or raise the home anxiety. Table 1 lists what we wish to

3 bytes every 30 seconds.

in a specific file.

light sensors.

automatically recognize.

**4.3 Home automation sensors** 

(each sensor activation versus time).

**5. Fuzzy logic activities recognition approach** 

**5.1 Parameter and method elaboration** 


Table 1. Fuzzy List ADLS to be recognized by the telemonitoring platform

The first step for developing this approach is the Fuzzification of system outputs and inputs obtained from each sensor and subsystem.

From Anason subsystem three inputs are built. The first one is the sound environment classification, all detected sound class and expressions are labeled on a numerical scale according to their source. Nine membership functions are set up in this numerical scale according to sound sources as it is in table 2.


Table 2. Fuzzy sets defined for the ANASON classification input

Two other inputs are associated to each SNR calculated on each microphone (two microphones are used in the current application), and these inputs are split into three fuzzy levels: low, medium and high.

The wearable terminal RFpat produce five inputs; Heart rate for which three fuzzy levels are specified normal, low and high; Activity which has four fuzzy sets: immobile, rest, normal and agitation; Posture is represented by two membership functions standing up / sitting down and lying; Fall and call have also two fuzzy levels: Fall/Call and No Fall/Call.

The defined area of each membership function associated to heart rate or activity is adapted to each monitored elderly person. In our application we use only posture, and activity inputs.

A Fuzzy Logic Approach for Remote Healthcare

Fig. 4. software implementation design

**6. DSS integration system** 

rules which produced them are displayed on the main panel.

each DSS is determined by the occurrence of false and undetected alarms.

Monitoring by Learning and Recognizing Human Activities of Daily Living 31

by using a specific language, understandable by the telemonitoring system. This framework also allows for rules to be added, deleted, or modified to fit each particular resident based on knowledge about their typical daily activities, physical status, cognitive status, and age. The software implementation is validated with many experimental tests. The results and the

The decision of this multimodal data fusion platform is sent to a real time decision integration system. This integration is performed by a multi-agent system (MAS) in which each agent coordinates separately with a decision support systems (DSS). The pertinence of

The agent delegates the decisional task to its corresponding DSS. The out coming decisions' data are then formatted by the agent in an abstract decision report. This report format is recognized in the whole system and enables a central agent to make the final decision. A real-time negotiation of the decisions is able to improve the usage of appropriate resources within an acceptable response time. Thus, this multi-agent system architecture enables these DSS to have uniform view of the decision concept and to exchanges both knowledge and

For each infrared sensor Ci a counter of motion detection with three fuzzy levels (low, medium, high) is associated, and a global one for all infrared sensors.

The time input has five membership functions morning, noon, afternoon, evening and night which are also adapted to patient habits.

For each main machine in the house a change state sensor S device,s name is associated. It has two membership functions turn on and turn off. One debit sensor for water is included in our application. Three membership functions characterize this sensor, low, medium and high. The output of our fuzzy logic ADL recognition contains some activities which are selected from the table I. They are Sleeping (S), Getting up (GU), Toileting (T), Bathing (B), Washing hands (WH), Washing dishes (WD), Doing laundry (DL), Cleaning (CL), Going out of home (GO), Enter home (EH), Walking (W), Standing up (SU), Setting down (SD),Laying (L), Resting (R), Watching TV (WT) and Talking on telephone (TT). These membership functions are ordered, firstly according to the area where they maybe occur and secondly according to the degree of similarity between them.

The next step of our fuzzy logic approach is the fuzzy inference engine which is formulated by a set of fuzzy IF-THEN rules. This second stage uses domain expert knowledge regarding activities to produce a confidence in the occurrence of an activity. Rules allow the recognition of common performances of an activity, as well as the ability to model special cases. An example fuzzy rule for alarm detection is:

*If (Anason is Machine sound) and (Activity is motion) and (COverall is high) and (CB is high) and (C5 is high) and (Svacuum is turn on) Then (ADLs is Cleaning).* 

A confidence factor is accorded to each rule and in order to aggregate these rules we have the choice between Mamdani or Sugeno approaches available under our fuzzy logic component. After rules aggregation the Defuzzification is performed by the centroid of area for the ADLs output*.*

#### **5.2 Software implementation**

Figure 4 provides a synoptic block-diagram scheme of the software architecture of the ADL recognition platform; it is implemented under LabwindowsCVI and C++ software. It is developed in a form of design component. We can distinguish three main components, the acquisition module, the synchronization module and the fuzzy inference component.

It can run off-line by reading data from a data base or online by processing in real time data acquired via the acquisition module. To avoid the loss of data, a real time module with two multithreading tasks is integrated in the synchronization component. The platform is now synchronized on Gardien subsystem because of his smallest sampling rate (2 Hz) and periodicity. Indeed in some situations the RFpat system may be not used by the elderly person, namely if no recommendations relative to its cardiac watch or a particular risk of fall are given by the Doctor.

The telemonitoring system with its Fuzzy tools allows the easy configuration of input intervals of fuzzification, the writing of fuzzy rules and the configuration of the defuzzification method. The general interface of the system allows to build up membership functions of inputs and outputs and displaying them. We could also write rules on text file

For each infrared sensor Ci a counter of motion detection with three fuzzy levels (low,

The time input has five membership functions morning, noon, afternoon, evening and night

For each main machine in the house a change state sensor S device,s name is associated. It has two membership functions turn on and turn off. One debit sensor for water is included in our application. Three membership functions characterize this sensor, low, medium and high. The output of our fuzzy logic ADL recognition contains some activities which are selected from the table I. They are Sleeping (S), Getting up (GU), Toileting (T), Bathing (B), Washing hands (WH), Washing dishes (WD), Doing laundry (DL), Cleaning (CL), Going out of home (GO), Enter home (EH), Walking (W), Standing up (SU), Setting down (SD),Laying (L), Resting (R), Watching TV (WT) and Talking on telephone (TT). These membership functions are ordered, firstly according to the area where they maybe occur and secondly

The next step of our fuzzy logic approach is the fuzzy inference engine which is formulated by a set of fuzzy IF-THEN rules. This second stage uses domain expert knowledge regarding activities to produce a confidence in the occurrence of an activity. Rules allow the recognition of common performances of an activity, as well as the ability to model special

*If (Anason is Machine sound) and (Activity is motion) and (COverall is high) and (CB is high) and (C5*

A confidence factor is accorded to each rule and in order to aggregate these rules we have the choice between Mamdani or Sugeno approaches available under our fuzzy logic component. After rules aggregation the Defuzzification is performed by the centroid of area

Figure 4 provides a synoptic block-diagram scheme of the software architecture of the ADL recognition platform; it is implemented under LabwindowsCVI and C++ software. It is developed in a form of design component. We can distinguish three main components, the

It can run off-line by reading data from a data base or online by processing in real time data acquired via the acquisition module. To avoid the loss of data, a real time module with two multithreading tasks is integrated in the synchronization component. The platform is now synchronized on Gardien subsystem because of his smallest sampling rate (2 Hz) and periodicity. Indeed in some situations the RFpat system may be not used by the elderly person, namely if no recommendations relative to its cardiac watch or a particular risk of fall

The telemonitoring system with its Fuzzy tools allows the easy configuration of input intervals of fuzzification, the writing of fuzzy rules and the configuration of the defuzzification method. The general interface of the system allows to build up membership functions of inputs and outputs and displaying them. We could also write rules on text file

acquisition module, the synchronization module and the fuzzy inference component.

medium, high) is associated, and a global one for all infrared sensors.

which are also adapted to patient habits.

according to the degree of similarity between them.

cases. An example fuzzy rule for alarm detection is:

*is high) and (Svacuum is turn on) Then (ADLs is Cleaning).* 

for the ADLs output*.*

are given by the Doctor.

**5.2 Software implementation** 

Fig. 4. software implementation design

by using a specific language, understandable by the telemonitoring system. This framework also allows for rules to be added, deleted, or modified to fit each particular resident based on knowledge about their typical daily activities, physical status, cognitive status, and age. The software implementation is validated with many experimental tests. The results and the rules which produced them are displayed on the main panel.

### **6. DSS integration system**

The decision of this multimodal data fusion platform is sent to a real time decision integration system. This integration is performed by a multi-agent system (MAS) in which each agent coordinates separately with a decision support systems (DSS). The pertinence of each DSS is determined by the occurrence of false and undetected alarms.

The agent delegates the decisional task to its corresponding DSS. The out coming decisions' data are then formatted by the agent in an abstract decision report. This report format is recognized in the whole system and enables a central agent to make the final decision. A real-time negotiation of the decisions is able to improve the usage of appropriate resources within an acceptable response time. Thus, this multi-agent system architecture enables these DSS to have uniform view of the decision concept and to exchanges both knowledge and

A Fuzzy Logic Approach for Remote Healthcare

inner learning procedure of such an agent.

**6.2.1 General operating principle** 

**6.2.2 Definition of the central agent tasks** 

agents. The conative function consists of making final decisions.

rules may be defined.

**6.2 Real-time scheduling of the collective decision process** 

Monitoring by Learning and Recognizing Human Activities of Daily Living 33

During this second wait window, the received message may be SEND decisions. As they do not concern the launched consensus, they are placed in the wait queue. The response messages are called CALL BACK decisions. At the end of the second wait window, the central agent computes the global pertinence of the received CALL BACK decisions. If the pertinence threshold is reached, the trigger decision is confirmed otherwise it is rejected and a learning procedure is sent to the responsible agent. In this article, we do not detail the

One of the major problems in the field of multi-agent systems is the need for methods and tools that facilitate the development of systems of this kind. In fact, the acceptance of multiagent system development methods in industry depends on the existence of the necessary tools to support the analysis, design and implementation of agent-based software. The emergence of useful real-time artificial intelligence systems makes the multi-agent system especially appropriate for development in a real-time environment (Julian and Botti, 2004). Furthermore, the response time of the DSS in a remote healthcare monitoring system is a central issue. Unfortunately the DSS studied in this context does not give a real-time response. For this reason we aim to control, as much as possible, the response time of their encapsulating Agents. The Gaia role model we presented in section 3 guaranties that the agent encapsulation of a DSS makes its response time transparent to the other agents.

This work has focused on a time-critical environment in which the acting systems can be monitored by intelligent agents which require real-time communication in order to better achieve the system's goal, which is detecting, as fast as possible, the distress situation of the patient. The works of (Julian and Botti, 2004) define a real-time agent as an agent with temporal restrictions in some of its responsibilities or tasks. According to this same work, a real-time multi-agent system is one where at least one of its agents is a real-time agent. The central agent is the unique decision output of our system. We will apply these definitions by focusing on the real-time scheduling of the central agent tasks. Firstly the different tasks of this agent must be defined. Subsequently, diverse scenarios and the priority assignation

As explained previously, the central agent receives all the decision reports in the system. The first main issue is thus the scheduling of the treatment of these messages. For each decision received the central agent chooses the concerned agents and assigns a response deadline to each one, based on the degree of expertise of the concerned agent in the modalities used. We propose a scheduling model that enables the reaching of a consensus between the different concerned agents while respecting the defined response deadlines.

As described in figure 6, an agent has two main functions: conative and cognitive. In the case of the central agent, the cognitive function consists of communicating with the other

intelligence, even if they implement several decisional techniques (Neural networks, fuzzy logic). In a remote healthcare monitoring system, we need such a solution in order to understand the behavior of the patient and the state of its domicile. Then, we can make the system evolve according to the analyzed behavior.

#### **6.1 Decision abstraction and priority assignation**

In intelligent remote healthcare monitoring, a decision support system uses the data flow of several modalities to generate decisions about the patient's situation. To standardize the decision concept, we classify the generated decisions by the modalities used. The considered modalities in our system are: sound, speech, physiological data (e.g. activeness and pulse rate), actimetric data (localization, falls), video, sensor states and alarm calls. Generally, every decision is based on global pertinence calculated by combining the pertinence affected to each decision modality. For a d decision, the global pertinence is:

$$\mathbf{G}p(d) = \sum\_{mi} p\_i(d) \cdot \mathbf{c}i \tag{10}$$

Where: *mi* is the modalities used for the decision *d*, *pi* is the pertinence of the decision *d* according to the modality *mi*, *ci* is the coefficient of the modality *mi* accorded by the DSS.

When a DSS generates a decision, it sends the data concerning this decision to its encapsulating agent. The agent reorganizes these data in a decision report (type, pertinence, arrival date …), which it then sends to the central agent.

The collective decision is made in two phases:


$$p\_i(d) = \sum\_{m\_j \text{ and}} A\_{ij} \cdot c\_j \tag{11}$$

Where *mj* is the modalities used in the trigger decision *d*, *cj* is the corresponding coefficient for each modality, *Aij* is the affinity of the agent *i* for the modality *mj.*

During this second wait window, the received message may be SEND decisions. As they do not concern the launched consensus, they are placed in the wait queue. The response messages are called CALL BACK decisions. At the end of the second wait window, the central agent computes the global pertinence of the received CALL BACK decisions. If the pertinence threshold is reached, the trigger decision is confirmed otherwise it is rejected and a learning procedure is sent to the responsible agent. In this article, we do not detail the inner learning procedure of such an agent.

#### **6.2 Real-time scheduling of the collective decision process**

One of the major problems in the field of multi-agent systems is the need for methods and tools that facilitate the development of systems of this kind. In fact, the acceptance of multiagent system development methods in industry depends on the existence of the necessary tools to support the analysis, design and implementation of agent-based software. The emergence of useful real-time artificial intelligence systems makes the multi-agent system especially appropriate for development in a real-time environment (Julian and Botti, 2004). Furthermore, the response time of the DSS in a remote healthcare monitoring system is a central issue. Unfortunately the DSS studied in this context does not give a real-time response. For this reason we aim to control, as much as possible, the response time of their encapsulating Agents. The Gaia role model we presented in section 3 guaranties that the agent encapsulation of a DSS makes its response time transparent to the other agents.

#### **6.2.1 General operating principle**

32 Fuzzy Logic – Emerging Technologies and Applications

intelligence, even if they implement several decisional techniques (Neural networks, fuzzy logic). In a remote healthcare monitoring system, we need such a solution in order to understand the behavior of the patient and the state of its domicile. Then, we can make the

In intelligent remote healthcare monitoring, a decision support system uses the data flow of several modalities to generate decisions about the patient's situation. To standardize the decision concept, we classify the generated decisions by the modalities used. The considered modalities in our system are: sound, speech, physiological data (e.g. activeness and pulse rate), actimetric data (localization, falls), video, sensor states and alarm calls. Generally, every decision is based on global pertinence calculated by combining the pertinence affected

> () () *i*

*m*

Where: *mi* is the modalities used for the decision *d*, *pi* is the pertinence of the decision *d* according to the modality *mi*, *ci* is the coefficient of the modality *mi* accorded by the DSS.

When a DSS generates a decision, it sends the data concerning this decision to its encapsulating agent. The agent reorganizes these data in a decision report (type, pertinence,

 Phase 1: the central agent starts the wait window of phase-1. The duration of the wait window depends on the trigger decision data (agent affinity, modalities used …). In this paper, we do not detail the computing algorithm of the waiting duration. The decision messages received in phase-1 are called SEND decisions. A SEND decision is a spontaneous decision. It is not a response to a previous request. In the case of a trigger decision, we also define the pertinence threshold. The arriving decision reports during this first wait window are fused with the trigger decision. If the final decision's pertinence surpasses the threshold, the decision is confirmed as an alert. If the wait window is terminated without attaining the pertinence threshold, the central agent

 Phase 2: the central agent starts a new wait window. During this wait window, a realtime consensus is launched among the agents concerned by the trigger decision modalities. For this purpose, the central agent assigns to each concerned agent a

> *j i ij j m d p d Ac*

Where *mj* is the modalities used in the trigger decision *d*, *cj* is the corresponding coefficient

( )

*i i*

*Gp d p d c* (10)

(11)

system evolve according to the analyzed behavior.

**6.1 Decision abstraction and priority assignation** 

to each decision modality. For a d decision, the global pertinence is:

arrival date …), which it then sends to the central agent.

The collective decision is made in two phases:

starts the second phase of decision.

consensus priority. This is computed as follows:

for each modality, *Aij* is the affinity of the agent *i* for the modality *mj.*

This work has focused on a time-critical environment in which the acting systems can be monitored by intelligent agents which require real-time communication in order to better achieve the system's goal, which is detecting, as fast as possible, the distress situation of the patient. The works of (Julian and Botti, 2004) define a real-time agent as an agent with temporal restrictions in some of its responsibilities or tasks. According to this same work, a real-time multi-agent system is one where at least one of its agents is a real-time agent. The central agent is the unique decision output of our system. We will apply these definitions by focusing on the real-time scheduling of the central agent tasks. Firstly the different tasks of this agent must be defined. Subsequently, diverse scenarios and the priority assignation rules may be defined.

As explained previously, the central agent receives all the decision reports in the system. The first main issue is thus the scheduling of the treatment of these messages. For each decision received the central agent chooses the concerned agents and assigns a response deadline to each one, based on the degree of expertise of the concerned agent in the modalities used. We propose a scheduling model that enables the reaching of a consensus between the different concerned agents while respecting the defined response deadlines.

#### **6.2.2 Definition of the central agent tasks**

As described in figure 6, an agent has two main functions: conative and cognitive. In the case of the central agent, the cognitive function consists of communicating with the other agents. The conative function consists of making final decisions.

A Fuzzy Logic Approach for Remote Healthcare

shortest absolute deadline has the highest priority.

**6.2.4 Queue priority and message selection** 

**6.2.5 Global scheduling of the central agent** 

Fig. 7. Real-time scheduling of the central agent.

assignment (Lehoczky, 1990).

wait queue.

Monitoring by Learning and Recognizing Human Activities of Daily Living 35

The BE queue is FIFO scheduled (First In First Out). There is no deadline or priority consideration in this queue. The CALL BACK and the SEND queue are EDF scheduled (George et al., 1996). EDF is the preemptive version of Earliest Deadline First non idling scheduling. EDF schedules the tasks according to their absolute deadlines: the task with the

Each message deadline must be determined before being classified in a wait queue. For this reason the Deadline assignation task, the message classification task and the message reception task must be fused. In fact, when a message arrives, the message reception task is activated. It cannot then be preempted before assigning the message to its corresponding

The message queues have dynamic priorities. This priority is assigned by a phase manager task. In phase-1, the SEND queue has the highest priority. In phase-2, the CALL BACK queue has the highest priority. While the message buffer is not empty, the message execution task's state is *Ready*. When it passes to execution, it selects the shortest deadline message from the highest priority queue. During the wait window of phase-1, the received SEND must be executed first. Thus we assign the highest priority to the SEND queue. When this wait window is closed, the decision task gets the highest priority. The CALL BACK queue has the highest priority in phase-2. Thus a phase cannot be terminated until the

The main scheduling algorithm of the central agent is FP/HPF. FP/HPF denotes the preemptive Fixed Priority Highest Priority First algorithm with an arbitrary priority

corresponding wait queue is empty and all the received decisions fused.

This classification leads us to this list of tasks assigned to the central agent:


Each task is executed according to the automaton described in figure 6.

Fig. 6. Execution states of the central agent tasks.

#### **6.2.3 Message classification**

The central agent message buffer consists of 3 different wait queues (WQ): the CALL BACK queue, for the CALL BACK decision messages, the SEND queue, for the SEND decision message and the Best Effort queue, for the other communication messages (decisions, service requests …)

The BE queue is FIFO scheduled (First In First Out). There is no deadline or priority consideration in this queue. The CALL BACK and the SEND queue are EDF scheduled (George et al., 1996). EDF is the preemptive version of Earliest Deadline First non idling scheduling. EDF schedules the tasks according to their absolute deadlines: the task with the shortest absolute deadline has the highest priority.

Each message deadline must be determined before being classified in a wait queue. For this reason the Deadline assignation task, the message classification task and the message reception task must be fused. In fact, when a message arrives, the message reception task is activated. It cannot then be preempted before assigning the message to its corresponding wait queue.

#### **6.2.4 Queue priority and message selection**

34 Fuzzy Logic – Emerging Technologies and Applications







The central agent message buffer consists of 3 different wait queues (WQ): the CALL BACK queue, for the CALL BACK decision messages, the SEND queue, for the SEND decision message and the Best Effort queue, for the other communication messages (decisions,

decision is made. Its main role is changing the priority of central agent tasks.

Each task is executed according to the automaton described in figure 6.

Fig. 6. Execution states of the central agent tasks.

**6.2.3 Message classification** 

service requests …)

This classification leads us to this list of tasks assigned to the central agent:



in the highest priority wait queue to the fusion buffer.

message in the appropriate wait queue.

of the central agent itself.

Cognitive tasks:

Conative tasks:

decision)

classification

The message queues have dynamic priorities. This priority is assigned by a phase manager task. In phase-1, the SEND queue has the highest priority. In phase-2, the CALL BACK queue has the highest priority. While the message buffer is not empty, the message execution task's state is *Ready*. When it passes to execution, it selects the shortest deadline message from the highest priority queue. During the wait window of phase-1, the received SEND must be executed first. Thus we assign the highest priority to the SEND queue. When this wait window is closed, the decision task gets the highest priority. The CALL BACK queue has the highest priority in phase-2. Thus a phase cannot be terminated until the corresponding wait queue is empty and all the received decisions fused.

#### **6.2.5 Global scheduling of the central agent**

The main scheduling algorithm of the central agent is FP/HPF. FP/HPF denotes the preemptive Fixed Priority Highest Priority First algorithm with an arbitrary priority assignment (Lehoczky, 1990).

Fig. 7. Real-time scheduling of the central agent.

A Fuzzy Logic Approach for Remote Healthcare

suppose that the message buffer is initially empty.

Fig. 9. ADLs recognition experiment for a stream data.

**7. Experimentation and results** 

which starts a new phase by changing the priority of the other tasks.

Monitoring by Learning and Recognizing Human Activities of Daily Living 37

During the phase-1 decision process, the CA receives two SEND messages. The reception task is preempted because it has a lower priority. In phase-2, A1, A2, A4 and A5 are involved in the consensus (a choice based on the trigger decision modalities). A SEND and 3 CALL BACK decisions are received (positive: A1 and A5, negative: A4). The final fusion reaches the pertinence threshold. Two learning procedures are sent to A4 and A2. We

The phase manager task is responsible for changing the priority of the central Agent tasks. We can observe on figure 8 the priority assigned to each task at the start of each new phase. The task manager is activated at the end of the wait windows to hand over to the decision task. At the end of its treatment, the decision task hands back to the phase manager task

The proposed method was experimentally achieved on a simulated data in order to demonstrate its effectiveness. This simulation gives very promising results for the ADLs recognition. Figure 9 shows results for a stream of a data. This fist study was devoted to the evaluation of the system by taking into account rules used in this fuzzy inference system.

In table 2, we present the priority evolution of each task during the different steps of the 2 phase collective decision (the higher the number, the higher the priority). The phase manager task always has the highest priority. In fact, it is responsible for changing the system phase and the priority assignation.

#### **6.2.6 Scheduling sample**

In figure 8, we present a scheduling sample in a system composed of a central agent (CA) and five other agents (A1, A2, A3, A4, A5). The red arrows represent the movement of the task to the ready state. Here we present the priority assigned to each task at the beginning of each phase. We suppose that the message wait queues are initially empty.


Table 3. Priority variation of the central agent tasks

Fig. 8. Temporal diagram of a scheduling sample

Our sample scenario goes through these stages: a trigger decision from A3 is received. The execution task treats the received trigger and then requests that the phase manager start a new collective decision process. The phase manager starts the first phase. It opens a new wait window and changes the priority of the CA tasks. During phase-1, two SEND decisions are received (from A1 and A4). The first wait window is terminated by the phase manager task.

The highest priority is assigned to the decision task. The pertinence threshold is not reached. The phase manager task starts the second phase. The highest priority in this task is accorded to the send task in order to allow the CA to activate the consensus.

During the phase-1 decision process, the CA receives two SEND messages. The reception task is preempted because it has a lower priority. In phase-2, A1, A2, A4 and A5 are involved in the consensus (a choice based on the trigger decision modalities). A SEND and 3 CALL BACK decisions are received (positive: A1 and A5, negative: A4). The final fusion reaches the pertinence threshold. Two learning procedures are sent to A4 and A2. We suppose that the message buffer is initially empty.

The phase manager task is responsible for changing the priority of the central Agent tasks. We can observe on figure 8 the priority assigned to each task at the start of each new phase. The task manager is activated at the end of the wait windows to hand over to the decision task. At the end of its treatment, the decision task hands back to the phase manager task which starts a new phase by changing the priority of the other tasks.

#### **7. Experimentation and results**

36 Fuzzy Logic – Emerging Technologies and Applications

In table 2, we present the priority evolution of each task during the different steps of the 2 phase collective decision (the higher the number, the higher the priority). The phase manager task always has the highest priority. In fact, it is responsible for changing the

In figure 8, we present a scheduling sample in a system composed of a central agent (CA) and five other agents (A1, A2, A3, A4, A5). The red arrows represent the movement of the task to the ready state. Here we present the priority assigned to each task at the beginning of

reception 4 4 2 3 1 Send 1 1 3 4 3 decision 2 2 4 1 4 execution 3 3 1 2 2 phase manager 5 5 5 5 5

Our sample scenario goes through these stages: a trigger decision from A3 is received. The execution task treats the received trigger and then requests that the phase manager start a new collective decision process. The phase manager starts the first phase. It opens a new wait window and changes the priority of the CA tasks. During phase-1, two SEND decisions are received (from A1 and A4). The first wait window is terminated by the

The highest priority is assigned to the decision task. The pertinence threshold is not reached. The phase manager task starts the second phase. The highest priority in this task is accorded

to the send task in order to allow the CA to activate the consensus.

Phase-1 Phase-2 *wait Decision wait Decision* 

each phase. We suppose that the message wait queues are initially empty.

*trigger*

system phase and the priority assignation.

Task *Wait For* 

Table 3. Priority variation of the central agent tasks

Fig. 8. Temporal diagram of a scheduling sample

phase manager task.

**6.2.6 Scheduling sample** 

The proposed method was experimentally achieved on a simulated data in order to demonstrate its effectiveness. This simulation gives very promising results for the ADLs recognition. Figure 9 shows results for a stream of a data. This fist study was devoted to the evaluation of the system by taking into account rules used in this fuzzy inference system.

Fig. 9. ADLs recognition experiment for a stream data.

A Fuzzy Logic Approach for Remote Healthcare

Helsinki, Finland, 1998.

NJ 1997.

4:87-100, 1972.

2009, pp. 3501-3504.

Monitoring by Learning and Recognizing Human Activities of Daily Living 39

Elger G. & Furugren B., "smartbo",an ict an computer-based demonstration home for

George, L., Rivierre, N., Spuri, M.: Preemptive and non-preemptive real-time uniprocessor

Hoppenot P., Boudy J., Delarue S., Baldinger J.-L. , Colle E., ''Assistance to the maintenance in

Jang J.S.R., Sun C. T. & Mizutani E., Neuro-Fuzzy and Soft Computing :A Computational

Julian V., Botti V., Developing real-time multi-agent systems. Integr. Comput.-Aided Eng.

Keller J.M. & Krishnapuram R., "Fuzzy set methods in computer vision," In R.R. Yager and

Lalande A., Legrand L., Walker P. M., Jaulent M. C., Guy F., Cottin Y. & Brunotte F.,

Lehoczky J.P., Fixed priority scheduling of periodic task sets with arbitrary deadlines. Proc. 11th IEEE Real-Time Systems Symposium, FL, USA, pp. 201-209, 5-7 Dec. 1990. Mandal D.P., Murthy C. A. & Pal S. K., "Formulation of a multivalued recognition system," IEEE Transactions on Systems, Man, and Cybernetics, 22:607–620 1992. Mason D., Linkens D. & Edwards N., Self-learning fuzzy logic control in medicine, Proc.

Medjahed H., Istrate D., Boudy J., Steenkeste F., Baldinger J.L., Belfeki I., Martins V. &

Noury N., Barralon P., Virone G., Boissy P., Hamel M. & Rumeau P.,A smart sensor based

Pal S.K. & Chakraborty B., "Fuzzy set theoretic measure for automatic feature evaluation," IEEE Transactions on Systems, Man, and Cybernetics, 16:754-760, 1986. Pao Y. H., "Adaptive Pattern Recognition and Neural Networks," Addison-Wesley, 1989. Pedrycz W., "Fuzzy sets in pattern recognition: methodology and methods," Pattern

Rougui J.E., Istrate D. & Souidene W., Audio Sound Event Identification for distress

Ruspini E. H., "A new approach to clustering," Inform, Control, 15(1):22-32, 1969. Shackle G.L., "Decision, Order and Time in Human Affairs," Cambridge Univ. Press

dynamic programming, Proc. AMIA Ann. Fall Symp. 1997, pp. 474–478. Lee S.W & Mase K., "Activity and location recognition using wearable sensors," IEEE

scheduling". INRIA, research Report 2966, Sept. 1996.

vol. 11,n° 2, p. 135-149, Amsterdam, April 2004.

Systems Kluwer Academic, pp. 121–145, 1992.

Pervasive Computing, 1(3):2432, 2002.

Springer-Verlag, Berlin 1997, pp. 300–303.

3289, Cancun, Mexico, September 2003.

Recognition, 23(1/2):121-146, 1990.

disabled people, in Proc. of the 3rd TIDE Congress : Technology for Inclusive Design and Equality Improving the Quality of Life for the European Citizen,

residence of handicapped or old people JESA – Volume 43 – N° 3/2009 pp. 315 – 335.

Approach to Learning and Machine Intelligence. Prentice Hall Upper Saddle River,

L.A. Zadeh, editors, An Introduction to Fuzzy logic Applications in Intelligent

Automatic detection of cardiac contours on MR images using fuzzy logic and

AIME'97, (E. Keravnou et al., eds.), Lecture Notes in Artificial Intelligence 1211,

Dorizzi B. , A Multimodal Platform for Database Recording and Elderly People Monitoring, BIOSIGNALS 2008, Jan 2008, Funchal-Madeira, Portugal, pp.385-392. Mizumoto M., Toyoda J. & Tanaka K., "General formulation of formal grammars," Info Sci.,

on rules and its evaluation in daily routines, in Proc of the IEEE-EMBC, pages 3286-

situations and context awareness, EMBC2009, September 2-6, Minneapolis, USA,

The used strategy consisted in realizing several tests with different combination rules, and based on obtained results one rule is added to the selected set of rules in order to get the missed detection. With this strategy good results are reached for the ADL output (about 97% of good ADL detection).

The experimentation described here is preliminary but demonstrates that ubiquitous, simple sensor devices can be used to recognize activities of daily living from real homes. The system can be easily retrofitted in existing home environments with no major modifications or damage.

#### **8. Conclusion**

In this chapter we have explore the cutting-edge research and technologies in monitoring daily activities using a set of sensors deployed in the house. The objective of the research is to provide a feasible solution for improving care for elderly people, while significantly reducing the healthcare cost. Focusing on the open problem of multiple persons monitoring, we have used an optimal set of sensors, design an algorithm for ADL recognition based on fuzzy logic, and implement a prototype. This approach provides robust and high accuracy recognition rate. Assisting elderly persons in place will benefit from the results of this research. The next objective of this research is to use these identification activities for building a model for measuring the home anxiety, that increases or decreases according to the detection activity and the state of each device in the home.

#### **9. Acknowledgments**

This work is supported by the European Commission in the frame of the Seventh Framework Program (FP7/2007-2011) within the CompanionAble Project (grant agreement n. 216487).

#### **10. References**


The used strategy consisted in realizing several tests with different combination rules, and based on obtained results one rule is added to the selected set of rules in order to get the missed detection. With this strategy good results are reached for the ADL output (about 97%

The experimentation described here is preliminary but demonstrates that ubiquitous, simple sensor devices can be used to recognize activities of daily living from real homes. The system can be easily retrofitted in existing home environments with no major modifications

In this chapter we have explore the cutting-edge research and technologies in monitoring daily activities using a set of sensors deployed in the house. The objective of the research is to provide a feasible solution for improving care for elderly people, while significantly reducing the healthcare cost. Focusing on the open problem of multiple persons monitoring, we have used an optimal set of sensors, design an algorithm for ADL recognition based on fuzzy logic, and implement a prototype. This approach provides robust and high accuracy recognition rate. Assisting elderly persons in place will benefit from the results of this research. The next objective of this research is to use these identification activities for building a model for measuring the home anxiety, that increases or decreases according to

This work is supported by the European Commission in the frame of the Seventh Framework Program (FP7/2007-2011) within the CompanionAble Project (grant agreement

Adlassnig K. P., Fuzzy set theory in medical diagnosis, IEEE Tr. On Syst.,Man, and

Buckley,J.J , Eslami E, An introduction to fuzzy logic and fuzzy sets. Advances in Soft

Burges C. J. C., A tutorial on SVM for Pattern Recognition. Data Mining and Knowledge

Cowell R., Dawid A., Lauritzen S. & Spiegelhalter D., Probabilistic Networks and Expert

Doermann D. and Mihalcik D., A system approach to achieving carernet, an integrated and

Dreyfus G., Martinez J.M, Samuelides M., Gordon M., Badran F., Thiria S. & Hrault L., R´eseaux de neurones. M´ethodologie et applications, Eyrolles, 2002. Dunn J.C., A fuzzy relative of the isodata process and its use in detecting compact wellseperated clusters. IEEE Tran. on Systems, Man, and Cybernetics, pp. 32–57, 1973.

Bezdek J. C. & Pal S. K., "Fuzzy Models for Pattern Recognition," IEEE Press, 1992.

intelligent telecare system, IEEE Trans Biomed Eng, 2:1-9, 1998.

the detection activity and the state of each device in the home.

Cybernetics, March/April 1986,pp. 260–265.

Computing. Physica-Verlag, Germany, 2002.

Discovery, volume 2, 1998, pp. 121–167.

Systems, 1999, ISBN : 0-387-98767-3.

of good ADL detection).

or damage.

**8. Conclusion** 

**9. Acknowledgments** 

n. 216487).

**10. References** 


**3** 

*University of Zagreb,* 

*Croatia* 

**Application of Fuzzy Logic in** 

*Faculty of Food Technology and Biotechnology,* 

**Diet Therapy – Advantages of Application** 

Jasenka Gajdoš Kljusurić, Ivana Rumora and Želimir Kurtanjek

Computing, in its usual sense, is centred on manipulation of numbers and symbols. In contrasts, computing with linguistic variables is a methodology in which the object of computation are words and propositions drawn from a natural language, e.g., significant

Computing with words is inspired by the remarkable human capability to perform a wide variety of physical and mental tasks without any measurements and any computation. A basic difference between perception and measurements is that, in general, the measurements are crisp whereas perceptions are fuzzy (Zadech, 1965, 1994, 1997, 2001; Wirsam et al., 1997; Hahn et al., 1995, 1995a; Darmon et al., 2002). Most of traditional tools for formal modelling, reasoning, and computing are crisp, deterministic, and precise in character. This methodology is a part of mathematical theories of artificial intelligence (Lehmann et al., 1992; Klir et al. 1997; Ray et al., 2002). Instead of Boolean logic, fuzzy logic uses a collection of fuzzy variables defined by membership functions and inference rules

Human nutrition, considering the daily intake of energy and nutrients, is often explained by computing with words (Brown et al., 1990; Bingham, 1987; Zadech, 1996; Wirsam & Hahn, 1999; Teodorescu et al., 1999), for instance the final conclusion regarding an analysed diet plan can result with phrases as: "the intake of Na should be considerably reduced" or "the consumption of fruits and vegetables must be increased". An important nutritionist's task is to improve the dietary habits of the whole population, on the long term, which would help to decrease the frequency of cardio-vascular disease and the morbidity of many chronic diseases such as diabetes (Katamay et al., 2007; Mahan & Escot-Stump, 2007). Hypertension, or high blood pressure, is one of the major diseases of the modern society. Hypertension has no initial symptoms but can lead to long-term diseases and complications. If it's uncontrolled can cause arteriosclerosis, cerebrovascular accidents, myocardial infarction, and end-stage renal disease (Alderman, 1999) and because physivally devastating is called the "silent killer". It is well known that there is a direct and positive relationship between age and gender with increased prevalence and severity of hypertension. Burt et al. (1995) have published that hypertension is a huge problem for people aged 60–74 years, 72.6% of the African American population and

increase in price, small, large, far from recommendations, etc.

(Čerić & Dalbelo-Bašić, 2004; Gajdoš et al., 2001; Rumora et al., 2009).

**1. Introduction** 

Shafer G., "A Mathematical Theory of Evidence," Princeton Univ. Press 1979.


Zadeh L.A., Fuzzy sets as a basis for theory of possibility, Fuzzy Set Systems. pp. 3–28, 1978.

Zahlmann G., Scherf M. & Wegner A., A neurofuzzy classifier for a knowledge-based glaucoma monitor, Proc. AIME'97, (E. Keravnou et al., eds.), Lecture Notes in Artificial Intelligence 1211, Springer-Verlag, Berlin 1997, pp. 273–284.

## **Application of Fuzzy Logic in Diet Therapy – Advantages of Application**

Jasenka Gajdoš Kljusurić, Ivana Rumora and Želimir Kurtanjek *University of Zagreb, Faculty of Food Technology and Biotechnology, Croatia* 

#### **1. Introduction**

40 Fuzzy Logic – Emerging Technologies and Applications

activity monitoring. in Proc. 29th Annual International Computer Software and Applications Conference: COMPSAC, pages 335-340, Edinburgh, Scotland 2005. Zadeh L.A., Fuzzy sets as a basis for theory of possibility, Fuzzy Set Systems. pp. 3–28, 1978. Zahlmann G., Scherf M. & Wegner A., A neurofuzzy classifier for a knowledge-based

glaucoma monitor, Proc. AIME'97, (E. Keravnou et al., eds.), Lecture Notes in

Shafer G., "A Mathematical Theory of Evidence," Princeton Univ. Press 1979.

Sugeno M., Theory of fuzzy integrals and its applications. Doct. Thesis, Tokyo IT 1974. West G.A.W., Greenhill S. & Venkatesh S., A probabilistic approach to the anxious home for

Artificial Intelligence 1211, Springer-Verlag, Berlin 1997, pp. 273–284.

Computing, in its usual sense, is centred on manipulation of numbers and symbols. In contrasts, computing with linguistic variables is a methodology in which the object of computation are words and propositions drawn from a natural language, e.g., significant increase in price, small, large, far from recommendations, etc.

Computing with words is inspired by the remarkable human capability to perform a wide variety of physical and mental tasks without any measurements and any computation. A basic difference between perception and measurements is that, in general, the measurements are crisp whereas perceptions are fuzzy (Zadech, 1965, 1994, 1997, 2001; Wirsam et al., 1997; Hahn et al., 1995, 1995a; Darmon et al., 2002). Most of traditional tools for formal modelling, reasoning, and computing are crisp, deterministic, and precise in character. This methodology is a part of mathematical theories of artificial intelligence (Lehmann et al., 1992; Klir et al. 1997; Ray et al., 2002). Instead of Boolean logic, fuzzy logic uses a collection of fuzzy variables defined by membership functions and inference rules (Čerić & Dalbelo-Bašić, 2004; Gajdoš et al., 2001; Rumora et al., 2009).

Human nutrition, considering the daily intake of energy and nutrients, is often explained by computing with words (Brown et al., 1990; Bingham, 1987; Zadech, 1996; Wirsam & Hahn, 1999; Teodorescu et al., 1999), for instance the final conclusion regarding an analysed diet plan can result with phrases as: "the intake of Na should be considerably reduced" or "the consumption of fruits and vegetables must be increased". An important nutritionist's task is to improve the dietary habits of the whole population, on the long term, which would help to decrease the frequency of cardio-vascular disease and the morbidity of many chronic diseases such as diabetes (Katamay et al., 2007; Mahan & Escot-Stump, 2007). Hypertension, or high blood pressure, is one of the major diseases of the modern society. Hypertension has no initial symptoms but can lead to long-term diseases and complications. If it's uncontrolled can cause arteriosclerosis, cerebrovascular accidents, myocardial infarction, and end-stage renal disease (Alderman, 1999) and because physivally devastating is called the "silent killer". It is well known that there is a direct and positive relationship between age and gender with increased prevalence and severity of hypertension. Burt et al. (1995) have published that hypertension is a huge problem for people aged 60–74 years, 72.6% of the African American population and

Application of Fuzzy Logic in Diet Therapy – Advantages of Application 43

a. fuzzification process – development of membership functions of fuzzy sets for input

b. Optimisation in the Pareto sense that implies that all observed variables (energy and all nutrients) and their compliance with recommendations for the observed variables have

c. defuzzification process (Rödder & Zimmermann, 1977; Wirsam et al., 1997) - presenting results as a crisp values and compared to standard linear programming (LP)

Basic of the fuzzy logic use will be used in (a) menu offer analysis and (b) menu planning. In the analysis and planning the main idea was to balance the daily energy and nutrient needs (Wirsam & Hahn, 1999; Wirsam et al., 1997) especially significant in the DASH diet (Gajdoš et al., 2001; Novák et al., 1999; Rumora et al, 2009). The algorithm used in the analysis and optimization is written in the programming system *W.R. Mathematica v.6.* 

Word "diet" implies the habitually amount and kind of food and drink taken by a person each day, so everyone is always on diet. From the medical point of view, diet means a prescribed selection of food. When this prescribed diet is related with therapy (what implies

Diet therapy is concentrated on a diet planned to meet specific requirements of the

Diet for hypertension is in the literature known as "DASH diet" (Dietary Approaches to Stop Hypertension). Basic DASH diet principle is a diversified diet. Studies have shown the Dietary Approaches to Stop Hypertension (DASH) is as effective for lowering blood pressure (BP) levels as the daily consumption of one prescription medication (Appel et al., 1997; Cook et al., 1995; Litle et al., 2004). Uncontrolled hypertension can cause arteriosclerosis, cerebrovascular accidents, myocardial infarction, and end-stage renal disease (Alderman, 1999) and because physically devastating is called the "silent killer" (Burt et al., 1995; Hajjar & Kotchen, 2003; Kumanyika, 1997). For a person with hypertension new eating style is a shock, and the following shock is a radical change in the costume eating habits (Cook et al., 1995). Effective DASH diet is abundant in dairy products (fat-free or low-fat), fruits and vegetables with a reduction in saturated fat, cholesterol, and total fat. However, long-term adherence to dietary modification is difficult for most people (Little et al., 2004) and, there is a need for interventions that help people adhere to dietary modifications. The DASH diet leads to an establishment of these goals. DASH diet that emphasizes consumption of fruits, vegetables, and low-fat dairy products, includes whole grains, poultry, fish, and nuts, and is reduced in fat, red meat, sweets, and sugar-containing

treatment) or a treatment of a disease – we are talking about diet therapy.

individual, including or excluding certain foods.

beverages with restriction of sodium intake.

This chapter follows the basics of use of fuzzy logic as:

information's as nutrient and energy intake;

equal importance

*(*Stachowicz & Beall, 1995).

**2. Diet therapy** 

**2.1 DASH diet** 

methodology.

50.6% of the Caucasian population had hypertension during 1988–1991 (Burt et al., 1995). Also African Americans, women older than 59 years, and older people have a higher prevalence and, even when treated, a greater severity of hypertension than Caucasians, men, and younger people (Hajjar & Kotchen, 2003 Appel, et al, 1997).

Nonpharmacological approach to treatment of the hypertension is currently in focus because of the higher awareness of the growing risk for the possible, future heart problems (MacMahon & Rogers, 1993; Appel, et al, 1997). For this reason, numerous researchers are focused on the clinically efficacious and cost effective interventions of dietary change (McCarron, 1998, Little et al., 2004).

Cook et al. (1995) presented that sustained reduction of 2 mmHg in diastolic blood pressure throughout lifestyle modifications, would result in (i) a 17% decrease in the prevalence of hypertension, (ii) as well as a 6% reduction in the risk of coronary heart disease, in elderly population. Alarming is the forecasting mentioned in Little et al. (2004) that the life expectation is decreasing by increment of blood pressure. Nutrition-based approaches are recommended as a first-line therapy for the prevention of the hypertension. Most recommendations for lifestyle modifications are focused on reducing salt intake, weight loss, and moderation of alcohol consumption. Other dietary interventions, particularly modifying whole dietary patterns, might also effectively reduce blood pressure and thereby control hypertension (Siri-Tarino et al., 2010).

Food guidelines and nutrient intake recommendations are usually expressed as specific quantities (crisp values). In meal planning, crisp values are to rigorous limitations, such as restrictions on nutrient intake, like for instance, the limits for sodium in the DASH diet – 2300 mg/day. Crisp values define the exclusive affiliation in the set, yes or not (Boolean logic). If the daily sodium recommendations are defined as 2300 mg, the daily offer that contains for example, 2350 mg, is according to crisp logic decision completely unacceptable. The overload of 50 mg of sodium per day could be an acceptable overload, but this offer with 2.2% more sodium than recommended will be excluded if the crisp value is overdrawn (Rumora et al., 2009). Fuzzy logic is used to describe unreliable (imprecise) data and knowledge, using linguistic variables, such as slightly deficiency or surplus, much more or less of some nutrient, etc. (Gajdoš et al., 2001; Čerić & Dalbelo-Bašić 2007).

The theory of fuzzy logic in this chapter was used in the planning and management of expenses in social nourishment concerning also the nutritive structure of meals. Modelling and planning of nourishment include a number of unspecified characteristics, which are depended on nutrient offer and also on age, gender and profession of a person (concerning the physical activity level) or population group. Some recommended nutrient and energy intakes are given as single numbers (crisp values). But for most nutrients are also given the average requirements (AR), the lowest threshold intake (LTI) and the calculated population reference intake, PRI (DRI, 1999, 2001, 2001a, 2001b). These intervals and the values of LTI, AR and PRI do not represent the full reality, which is a continuous transition from critical low intake to adequate intake to excess or even toxic amounts. In this work the daily recommendations as crisp numbers are modelled as fuzzy sets (Wirsam et al., 1997, 1997a). The daily recommended intake (DRI) for each observed nutrient and energy intake is "softened" by introduction of membership function of fuzzy sets defined for each individual nutrient.

This chapter follows the basics of use of fuzzy logic as:


Basic of the fuzzy logic use will be used in (a) menu offer analysis and (b) menu planning.

In the analysis and planning the main idea was to balance the daily energy and nutrient needs (Wirsam & Hahn, 1999; Wirsam et al., 1997) especially significant in the DASH diet (Gajdoš et al., 2001; Novák et al., 1999; Rumora et al, 2009). The algorithm used in the analysis and optimization is written in the programming system *W.R. Mathematica v.6. (*Stachowicz & Beall, 1995).

#### **2. Diet therapy**

42 Fuzzy Logic – Emerging Technologies and Applications

50.6% of the Caucasian population had hypertension during 1988–1991 (Burt et al., 1995). Also African Americans, women older than 59 years, and older people have a higher prevalence and, even when treated, a greater severity of hypertension than Caucasians, men, and younger

Nonpharmacological approach to treatment of the hypertension is currently in focus because of the higher awareness of the growing risk for the possible, future heart problems (MacMahon & Rogers, 1993; Appel, et al, 1997). For this reason, numerous researchers are focused on the clinically efficacious and cost effective interventions of dietary change

Cook et al. (1995) presented that sustained reduction of 2 mmHg in diastolic blood pressure throughout lifestyle modifications, would result in (i) a 17% decrease in the prevalence of hypertension, (ii) as well as a 6% reduction in the risk of coronary heart disease, in elderly population. Alarming is the forecasting mentioned in Little et al. (2004) that the life expectation is decreasing by increment of blood pressure. Nutrition-based approaches are recommended as a first-line therapy for the prevention of the hypertension. Most recommendations for lifestyle modifications are focused on reducing salt intake, weight loss, and moderation of alcohol consumption. Other dietary interventions, particularly modifying whole dietary patterns, might also effectively reduce blood pressure and thereby

Food guidelines and nutrient intake recommendations are usually expressed as specific quantities (crisp values). In meal planning, crisp values are to rigorous limitations, such as restrictions on nutrient intake, like for instance, the limits for sodium in the DASH diet – 2300 mg/day. Crisp values define the exclusive affiliation in the set, yes or not (Boolean logic). If the daily sodium recommendations are defined as 2300 mg, the daily offer that contains for example, 2350 mg, is according to crisp logic decision completely unacceptable. The overload of 50 mg of sodium per day could be an acceptable overload, but this offer with 2.2% more sodium than recommended will be excluded if the crisp value is overdrawn (Rumora et al., 2009). Fuzzy logic is used to describe unreliable (imprecise) data and knowledge, using linguistic variables, such as slightly deficiency or surplus, much more or

The theory of fuzzy logic in this chapter was used in the planning and management of expenses in social nourishment concerning also the nutritive structure of meals. Modelling and planning of nourishment include a number of unspecified characteristics, which are depended on nutrient offer and also on age, gender and profession of a person (concerning the physical activity level) or population group. Some recommended nutrient and energy intakes are given as single numbers (crisp values). But for most nutrients are also given the average requirements (AR), the lowest threshold intake (LTI) and the calculated population reference intake, PRI (DRI, 1999, 2001, 2001a, 2001b). These intervals and the values of LTI, AR and PRI do not represent the full reality, which is a continuous transition from critical low intake to adequate intake to excess or even toxic amounts. In this work the daily recommendations as crisp numbers are modelled as fuzzy sets (Wirsam et al., 1997, 1997a). The daily recommended intake (DRI) for each observed nutrient and energy intake is "softened" by introduction of membership function of fuzzy sets defined for each individual

less of some nutrient, etc. (Gajdoš et al., 2001; Čerić & Dalbelo-Bašić 2007).

people (Hajjar & Kotchen, 2003 Appel, et al, 1997).

(McCarron, 1998, Little et al., 2004).

control hypertension (Siri-Tarino et al., 2010).

nutrient.

Word "diet" implies the habitually amount and kind of food and drink taken by a person each day, so everyone is always on diet. From the medical point of view, diet means a prescribed selection of food. When this prescribed diet is related with therapy (what implies treatment) or a treatment of a disease – we are talking about diet therapy.

Diet therapy is concentrated on a diet planned to meet specific requirements of the individual, including or excluding certain foods.

#### **2.1 DASH diet**

Diet for hypertension is in the literature known as "DASH diet" (Dietary Approaches to Stop Hypertension). Basic DASH diet principle is a diversified diet. Studies have shown the Dietary Approaches to Stop Hypertension (DASH) is as effective for lowering blood pressure (BP) levels as the daily consumption of one prescription medication (Appel et al., 1997; Cook et al., 1995; Litle et al., 2004). Uncontrolled hypertension can cause arteriosclerosis, cerebrovascular accidents, myocardial infarction, and end-stage renal disease (Alderman, 1999) and because physically devastating is called the "silent killer" (Burt et al., 1995; Hajjar & Kotchen, 2003; Kumanyika, 1997). For a person with hypertension new eating style is a shock, and the following shock is a radical change in the costume eating habits (Cook et al., 1995). Effective DASH diet is abundant in dairy products (fat-free or low-fat), fruits and vegetables with a reduction in saturated fat, cholesterol, and total fat.

However, long-term adherence to dietary modification is difficult for most people (Little et al., 2004) and, there is a need for interventions that help people adhere to dietary modifications. The DASH diet leads to an establishment of these goals. DASH diet that emphasizes consumption of fruits, vegetables, and low-fat dairy products, includes whole grains, poultry, fish, and nuts, and is reduced in fat, red meat, sweets, and sugar-containing beverages with restriction of sodium intake.

Application of Fuzzy Logic in Diet Therapy – Advantages of Application 45

Hahn and his co-workers (1995 & 1995a) have been the first that have applied fuzzy logic in defining nutrient intakes using membership functions. For each nutrient was determined a fuzzy set, μ (xi). The tendency is to achieve maximal value (value 1) of the membership function μ, for each observed nutrient, which would mean that the input of the nutrient is optimal (Hahn et al., 1995). In Croatia are accepted the recommended dietary intakes (DRIs) for nutrients given as a range of allowances described by crisp numbers, DRIs, or an interval of estimated safe and adequate daily dietary intake (ESADDI). As crisp values (Wirsam et al., 1997a; Gajdoš et al., 2001; Rumora et al., 2009; Teodorescu et al., 1999), these numbers

This is the crisp formulation of allowances and can be used, for example, as restrictions in linear optimisation. The corresponding fuzzy set *allowed intake* can be defined by a

,min ,max 1, ( ) 0,

Fuzzy sets are used to represent the inherent imprecision and fuzziness of food quantities and nutrient values as well as to model the gradual boundaries of the daily recommended values associated with each nutrient. Knowing that cardiovascular diseases are considered as one of the leading causes of today mortality, especially for men aged 31-50 years, who conducted low active way of life with a diet that is mainly consumption of ready to eat or fast food, and that small interventions in the nourishment can achieve significant positive

The process of transforming crisp values into grades of membership for linguistic terms of fuzzy sets comprises fuzzification. The membership function is used to associate a grade to each linguistic term. The fuzzification process is a modelling process where the membership functions of fuzzy sets for input information's as nutrient and energy intake are

Fuzzy membership functions are constructed to describe the range of nutrients intake from deficient to excess amounts. For optimisation three goal functions are considered: price, organic-chemical structure and meal preferences. Observing of two or more goal functions at the same time allows optimising in the Pareto sense. With the help of these sets, an evaluation as well as optimisation in the Pareto sense (considering the price, preferences and

This study shows that the use of the fuzzy sets can be utilised for Pareto optimisation by which multiple object optimisation is achieved. The fuzzy model represents recommended energy and nutrient intake more adequately then the Dietary Recommended Intake, DRI, intake presented as crisp values, as well as to obtain acceptable price and preferences of

*a aa*

*for unaceptable intake*

*for x x x*

 *xa,min* **≤** *xa* **≤** *xa,max* (1)

(2)

**3.1 Crisp and fuzzy interpretation of DRIs** 

characteristic membership function μ (xa):

**3.2 Fuzzification** 

development.

nutrient intake) is possible.

menu selection for a population group.

describe a range of allowed intake, *xa*, of a nutrient *a* as followed:

*a*

*x*

impact, fuzzy approach was used to plan daily menus.

Guidelines given by the DASH diet are valuable for those who know their daily intake, but the less troublesome step from the guidelines could be the reduction of sodium intake as well increase of fruit and vegetable consumption. Sometimes the first step is searching of readymade recipes based on the DASH diet guidelines (AHA, 2004). This is the reason way we have analysed such offers (recipes available from internet resources: AHA, 2004), what was the first goal in this work. The second goal was to propose – computer based menus that will help in the further menu planning. Having crisp values for daily needs it is possible to use them in computer-based planning of optimal menus with respect to agreed evidencebased dietary recommendations and guidelines.

Despite a reputation for genesis of cardiac disease, there is strong evidence for the cardiovascular benefits of saturated fats (McCarron, 1998) In 2010, a meta-analysis of prospective cohort studies including 348,000 subjects found no statistically significant relationship between cardiovascular disease and dietary saturated fat (Siri-Tarino et al, 2010) However, the authors noted that randomized controlled clinical trials in which saturated fat was replaced with polyunsaturated fat showed a reduction in heart disease, and that the ratio between polyunsaturated fat and saturated fat may be a key factor. In 2009, a systematic review of prospective cohort studies or randomized trials concluded that there was "insufficient evidence of association" between intake of saturated fatty acids and coronary heart disease, and pointed to strong evidence for protective factors such as vegetables and a Mediterranean diet and harmful factors such as trans fats and foods with a high glycemic index (Siri-Tarino et al., 2010). Pacific island populations who obtain 30-60% of their total caloric intake from fully saturated coconut fat have low rates of cardiovascular disease (McCarron, 1998).

#### **3. Fuzzy sets**

The foundation for the development of the fields of artificial intelligence and expert systems has become fuzzy set theory, especially in the applications of knowledge-based systems.

Fuzzy logic deals with reasoning that is approximate instead of fixed and exact. In contrast with Boolean logic theory, where binary sets have two-valued logic: true or false, fuzzy logic variables may have a truth value that ranges in degree between 0 and 1. Fuzzy logic has been extended to handle the concept of partial truth, where the truth value may range between completely true and completely false (Novák et al., 1999). Implying, when linguistic variables are used, these degrees may be managed by specific functions (Leventhal, et al, 1992).

While variables in mathematics usually take numerical values, in fuzzy logic applications, the non-numeric linguistic variables are often used to facilitate the expression of rules and facts (Zadech, 1996).

A linguistic variable such as *quality* may have a value such as *good* or its antonym *bad*. However, the great utility of linguistic variables is that they can be modified via linguistic hedges applied to primary terms. The linguistic hedges can be associated with certain functions. Linguistic variables are very often used in nutrition, ie. in analysis of nutrient intake, where an nutrient amount can be, sufficient, optimal or insufficiency. The application of fuzzy sets in nutrition will be explained in the following text.

#### **3.1 Crisp and fuzzy interpretation of DRIs**

44 Fuzzy Logic – Emerging Technologies and Applications

Guidelines given by the DASH diet are valuable for those who know their daily intake, but the less troublesome step from the guidelines could be the reduction of sodium intake as well increase of fruit and vegetable consumption. Sometimes the first step is searching of readymade recipes based on the DASH diet guidelines (AHA, 2004). This is the reason way we have analysed such offers (recipes available from internet resources: AHA, 2004), what was the first goal in this work. The second goal was to propose – computer based menus that will help in the further menu planning. Having crisp values for daily needs it is possible to use them in computer-based planning of optimal menus with respect to agreed evidence-

Despite a reputation for genesis of cardiac disease, there is strong evidence for the cardiovascular benefits of saturated fats (McCarron, 1998) In 2010, a meta-analysis of prospective cohort studies including 348,000 subjects found no statistically significant relationship between cardiovascular disease and dietary saturated fat (Siri-Tarino et al, 2010) However, the authors noted that randomized controlled clinical trials in which saturated fat was replaced with polyunsaturated fat showed a reduction in heart disease, and that the ratio between polyunsaturated fat and saturated fat may be a key factor. In 2009, a systematic review of prospective cohort studies or randomized trials concluded that there was "insufficient evidence of association" between intake of saturated fatty acids and coronary heart disease, and pointed to strong evidence for protective factors such as vegetables and a Mediterranean diet and harmful factors such as trans fats and foods with a high glycemic index (Siri-Tarino et al., 2010). Pacific island populations who obtain 30-60% of their total caloric intake from fully saturated coconut fat have low rates of cardiovascular

The foundation for the development of the fields of artificial intelligence and expert systems has become fuzzy set theory, especially in the applications of knowledge-based systems.

Fuzzy logic deals with reasoning that is approximate instead of fixed and exact. In contrast with Boolean logic theory, where binary sets have two-valued logic: true or false, fuzzy logic variables may have a truth value that ranges in degree between 0 and 1. Fuzzy logic has been extended to handle the concept of partial truth, where the truth value may range between completely true and completely false (Novák et al., 1999). Implying, when linguistic variables are used, these degrees may be managed by specific functions

While variables in mathematics usually take numerical values, in fuzzy logic applications, the non-numeric linguistic variables are often used to facilitate the expression of rules and

A linguistic variable such as *quality* may have a value such as *good* or its antonym *bad*. However, the great utility of linguistic variables is that they can be modified via linguistic hedges applied to primary terms. The linguistic hedges can be associated with certain functions. Linguistic variables are very often used in nutrition, ie. in analysis of nutrient intake, where an nutrient amount can be, sufficient, optimal or insufficiency. The

application of fuzzy sets in nutrition will be explained in the following text.

based dietary recommendations and guidelines.

disease (McCarron, 1998).

(Leventhal, et al, 1992).

facts (Zadech, 1996).

**3. Fuzzy sets** 

Hahn and his co-workers (1995 & 1995a) have been the first that have applied fuzzy logic in defining nutrient intakes using membership functions. For each nutrient was determined a fuzzy set, μ (xi). The tendency is to achieve maximal value (value 1) of the membership function μ, for each observed nutrient, which would mean that the input of the nutrient is optimal (Hahn et al., 1995). In Croatia are accepted the recommended dietary intakes (DRIs) for nutrients given as a range of allowances described by crisp numbers, DRIs, or an interval of estimated safe and adequate daily dietary intake (ESADDI). As crisp values (Wirsam et al., 1997a; Gajdoš et al., 2001; Rumora et al., 2009; Teodorescu et al., 1999), these numbers describe a range of allowed intake, *xa*, of a nutrient *a* as followed:

$$
\propto \chi\_{a,min} \lessapprox \chi\_a \lessapprox \chi\_{a,max} \tag{1}
$$

This is the crisp formulation of allowances and can be used, for example, as restrictions in linear optimisation. The corresponding fuzzy set *allowed intake* can be defined by a characteristic membership function μ (xa):

$$\mu(\mathbf{x}\_a) = \begin{cases} 1, \text{ for } \begin{array}{l} \mathbf{x}\_{a,\text{min}} \le \mathbf{x}\_a \le \mathbf{x}\_{a,\text{max}} \\ 0, \text{ for } \text{un acceptable intake} \end{array} \tag{2}$$

Fuzzy sets are used to represent the inherent imprecision and fuzziness of food quantities and nutrient values as well as to model the gradual boundaries of the daily recommended values associated with each nutrient. Knowing that cardiovascular diseases are considered as one of the leading causes of today mortality, especially for men aged 31-50 years, who conducted low active way of life with a diet that is mainly consumption of ready to eat or fast food, and that small interventions in the nourishment can achieve significant positive impact, fuzzy approach was used to plan daily menus.

#### **3.2 Fuzzification**

The process of transforming crisp values into grades of membership for linguistic terms of fuzzy sets comprises fuzzification. The membership function is used to associate a grade to each linguistic term. The fuzzification process is a modelling process where the membership functions of fuzzy sets for input information's as nutrient and energy intake are development.

Fuzzy membership functions are constructed to describe the range of nutrients intake from deficient to excess amounts. For optimisation three goal functions are considered: price, organic-chemical structure and meal preferences. Observing of two or more goal functions at the same time allows optimising in the Pareto sense. With the help of these sets, an evaluation as well as optimisation in the Pareto sense (considering the price, preferences and nutrient intake) is possible.

This study shows that the use of the fuzzy sets can be utilised for Pareto optimisation by which multiple object optimisation is achieved. The fuzzy model represents recommended energy and nutrient intake more adequately then the Dietary Recommended Intake, DRI, intake presented as crisp values, as well as to obtain acceptable price and preferences of menu selection for a population group.

Application of Fuzzy Logic in Diet Therapy – Advantages of Application 47

The shape of the fuzzy set presented on figure 1 is the so called "bell-shape". Beside the bellshape, commonly used shapes in nutrition evaluation and/or planning are: S and Z shape. Those two shapes depend on the preferred amounts of nutrient intakes (presented on Fig. 2).

µ

1

Fig. 2. Shape of a fuzzy set when the intake of the observed nutrient is preferred not be low

Example of the nutrient intake where low amounts are not preferred is the daily intake of dietary fibres. Nutrients that are not welcome in high amounts per day are alcohol and

Fuzzy approach in nutrition planning is based on the use of the linguistic approach and its application to solve decision problems with linguistic information (Buisson, 2008). Computing with Words (CW) is defined as use of linguistic computational techniques to process linguistic information. An example can be given if one considers an ordinal scale

T={T0="none", T1="Very Low", T2="Low", T3="Medium",

Reproducing the mentioned linguistic terms (eq. 6) on the daily intake of alcohol and connecting it with the Z shape of its fuzzy set, the terms used would be connected as

 T={T0="Preferred", T1="Medium", T2="Unacceptable"} (7) The approximate computational model processes the membership functions of the fuzzy terms and results in an aggregated fuzzy number. These aggregated fuzzy numbers do not necessarily belong to the initial set of linguistic terms. The ordering of the aggregated fuzzy values can be achieved by using a fuzzy ranking method to compare them. However, this comparison process can be quite complex and produce unreliable results, as it may: (i) involve considerable computations, (ii) produce inconsistency via respective fuzzy ranking methods, and (iii) generate counter-intuitive ranking outcomes for similar fuzzy numbers.

T4="High", T5="Very High", T6="Perfect"} (6)

**A2**

*µ(A1)* or, to be as lower as possible *µ(A2)*.

**A1**

cholesterol.

µ

1

follows:

**3.3 Defuzzification** 

with seven linguistic terms (T):

Objective of the research is to propose a method of modelling and optimization that will consider the daily expenses, meal preferences in different regions and the energy and nutrient requirements of some gender and age group**.** 

In the fuzzy set modelling of nutrients is important to construct the function following the basic properties of a fuzzy set (Dalbelo-Bašić, 2002; Buisson, 2008). Each membership function is defined by its core, height and support (Figure 1).

Fig. 1. Properties of a fuzzy set A.

In the construction of nutrient membership function of the following properties for fuzzy sets were used:

The core of fuzzy set A*, core(A)*, is a subset universal set X with the property μ<sup>A</sup> (x) = 1, ie

$$$$

The support of the fuzzy set A, *supp (A),* is a subset of the universal set X with nonzero membership grades ( μA(x)> 0), ie

$$\text{supp } (A) = \{ (\mathbf{x} \in \mathcal{X} \mid \mu\_A \text{ (}\mathbf{x} \succeq 1\text{)}\text{)}\tag{4}$$

The height of a fuzzy set, hgt(A), is the supremum (maximum) of the membership grades of A. So,

$$\text{Magt (A)} = \max\_{\text{x} \quad a \in \text{A}} \mu\_{A}(X) \tag{5}$$

A fuzzy set A is normal if the height equal to 1, hgt(A) = 1. Any set that is not normal is called subnormal.

Core and support of a fuzzy set are ordinary subsets of X, while the height is a real number from the interval [0, 1].

The shape of the fuzzy set presented on figure 1 is the so called "bell-shape". Beside the bellshape, commonly used shapes in nutrition evaluation and/or planning are: S and Z shape. Those two shapes depend on the preferred amounts of nutrient intakes (presented on Fig. 2).

Fig. 2. Shape of a fuzzy set when the intake of the observed nutrient is preferred not be low *µ(A1)* or, to be as lower as possible *µ(A2)*.

Example of the nutrient intake where low amounts are not preferred is the daily intake of dietary fibres. Nutrients that are not welcome in high amounts per day are alcohol and cholesterol.

#### **3.3 Defuzzification**

46 Fuzzy Logic – Emerging Technologies and Applications

Objective of the research is to propose a method of modelling and optimization that will consider the daily expenses, meal preferences in different regions and the energy and

In the fuzzy set modelling of nutrients is important to construct the function following the basic properties of a fuzzy set (Dalbelo-Bašić, 2002; Buisson, 2008). Each membership

core

In the construction of nutrient membership function of the following properties for fuzzy

The support of the fuzzy set A, *supp (A),* is a subset of the universal set X with nonzero

The height of a fuzzy set, hgt(A), is the supremum (maximum) of the membership grades of

A fuzzy set A is normal if the height equal to 1, hgt(A) = 1. Any set that is not normal is

Core and support of a fuzzy set are ordinary subsets of X, while the height is a real number

*XµA* (x=1)} (3)

height

*XµA* (x > 1)} (4)

*<sup>X</sup> µA*(*X*) (5)

The core of fuzzy set A*, core(A)*, is a subset universal set X with the property μ<sup>A</sup> (x) = 1, ie

support

*core (A)* ={(*x* 

*supp (A)* ={(*x* 

*hgt (A)* = *maxx*

nutrient requirements of some gender and age group**.** 

**A**

Fig. 1. Properties of a fuzzy set A.

membership grades ( μA(x)> 0), ie

sets were used:

µ

1

A. So,

called subnormal.

from the interval [0, 1].

function is defined by its core, height and support (Figure 1).

Fuzzy approach in nutrition planning is based on the use of the linguistic approach and its application to solve decision problems with linguistic information (Buisson, 2008). Computing with Words (CW) is defined as use of linguistic computational techniques to process linguistic information. An example can be given if one considers an ordinal scale with seven linguistic terms (T):

$$\begin{array}{l} \text{T}=\{\text{T}\_{0}=\text{''}\text{none}^{\prime\prime},\text{T}\_{1}=\text{''}\text{Very Low}^{\prime},\text{T}\_{2}=\text{''}\text{Low}^{\prime},\text{T}\_{3}=\text{''}\text{Medium}^{\prime}\} \\ \text{T}\_{4}=\text{''}\text{High}^{\prime},\text{T}\_{5}=\text{''}\text{Very High}^{\prime},\text{T}\_{6}=\text{''}\text{Perfect}^{\prime}\} \end{array} \tag{6}$$

Reproducing the mentioned linguistic terms (eq. 6) on the daily intake of alcohol and connecting it with the Z shape of its fuzzy set, the terms used would be connected as follows:

$$\mathbf{T} = \{ \mathbf{T}\_0 = \text{''Prefierend''}, \ \mathbf{T}\_1 = \text{''Medium''}, \ \mathbf{T}\_2 = \text{''Unacceptable''} \}\tag{7}$$

The approximate computational model processes the membership functions of the fuzzy terms and results in an aggregated fuzzy number. These aggregated fuzzy numbers do not necessarily belong to the initial set of linguistic terms. The ordering of the aggregated fuzzy values can be achieved by using a fuzzy ranking method to compare them. However, this comparison process can be quite complex and produce unreliable results, as it may: (i) involve considerable computations, (ii) produce inconsistency via respective fuzzy ranking methods, and (iii) generate counter-intuitive ranking outcomes for similar fuzzy numbers.

Application of Fuzzy Logic in Diet Therapy – Advantages of Application 49

Basic emphasis was on nutrients whose intake, in the DASH diet, is generally important in the treatment. Emphasis was on the control of the daily intake of energy, intake of fats, saturated fats, cholesterol, magnesium, potassium, calcium, sodium, dietary fibre, proteins

Total fat 27% of daily energy intake Saturated fat 6% of daily energy intake Protein 18% of daily energy intake Carbohydrate 55% of daily energy intake

\* 1,500 mg sodium was a lower goal tested and found to be even better for lowering blood pressure. It was particularly effective for middle-aged and older individuals, African Americans, and those who

Fuzzy logic modelling is applied for modelling and optimisation of nutritional requirements given by DASH diet guidelines that present crisp values, as presented in table 1 where are given crisp values that should be achieved for a daily intake based on 2,100 kcal (8790 kJ)

In order to visualize fuzzy concept, intake of a nutrient will be estimated with a value between 0 (not belonging to the set) and 1 (completely belongs). This value of belonging to a

The modelling of a fuzzy set followed the instruction of Wirsam and co-workers (1997) where 5 points are crucial in the fuzzy set construction. Those five points will be explained on the presented example for sodium intake (Figure 3). The value y is the value of the fuzzy value µ.

This approach in modelling of fuzzy set membership functions for the daily input was presented in some other studies what indicates the successful applicability (Wirsam &

Hahn, 1999; Wirsam et al., 1997; Gajdoš et al., 2001; Rumora et al.,, 2009).

set is defining the acceptability or unacceptability grade regarding the DASH diet.

Cholesterol 150 mg Sodium 2300\* mg Potassium 4700 mg Calcium 1250 mg Magnesium 500 mg Dietary Fibre 30 g

**4.1 Membership functions modelled according DASH guidelines** 

already had high blood pressure. g = grams; mg = milligrams Table 1. DASH diet guideline for a 2 100 kcal Eating Plan

Five points used in the construction of the fuzzy set: Fuzzy value for zero intake of a nutrient (y=0) Safe minimum limit of intake of a nutrient (y=0.9)

Safe upper limit of intake of a nutrient (y=0.9)

Optimal intake of a nutrient (y=1)

The toxic perilous area (y=0)

**DASH recommendations**  based on a daily eating plan of 2100 kcal (8790 kJ)

and carbohydrates.

**Observed nutrients in DASH diet** 

eating plan (AHA, 2004).

The process of producing a quantifiable result in fuzzy logic, given fuzzy sets and corresponding membership degrees is defuzzification. This means that for every possible value *µ*, should be given a result with a grade of membership that describes to what extent this value *µ* is reasonable to use. Defuzzification is a process of transformation of this fuzzy information into a single value *µ´* that will actually be applied in the decision making process. This transformation from a fuzzy set to a crisp number (defuzzification) is necessary because humans are more familiar with crisp values.

The goal, of using the fuzzy sets in nutrition is to optimize the diet so that the requirements for all observed nutrients are achieved. For example if there is too little dietary fibre and too much energy in the diet, adding wholemeal bread gives more dietary fibre but also more energy – so there is a conflict (Wirsam et al., 1997; Wirsam & Hahn, 1999; Teodorescu et al., 1999; McBride, 1997). To solve this conflict and to represent the logical "and" (because it is desirable to optimize both dietary fibre and energy), compromises are made (Wirsam & Hahn, 1999; Wirsam et al., 1999). Wirsam suggested the application of the product of the minimal membership vale and the harmonic mean to the fuzzy sets of the rest of observed nutrients, gives the name to the crisp value that defuzzifies the optimisation – the Prerow value (PV):

$$PV = \min\{\mu(\mathbf{x}\_i)\} \cdot (n - 1) / \left(\sum\_{i \neq i\_{\min}}^{n} \frac{1}{\mu(\mathbf{x}\_i)}\right) \tag{8}$$

μ(xi) are the fuzzy sets for *i* nutrients that are observed. So defined Prerow value is now a measure for how close on average one comes to the recommendations - or how healthy our food is. With the Prerow value one can decide whether a certain nutrition situation is better or worse than the other. Wirsam has graded the PV values (between 0 and 1) of a nutritive offer concerning their impact on health (Wirsam & Hahn, 1999; Wirsam et al., 1999). In accordance with the health impact, the preferred PV values are PV>07, and an acceptable meal or menu offer with balanced energy and nutrient offers. Those offers that result with PV > 0.9 would be considered as optimal offers with highly appreciated energy and content of nutrients. Prerow value, so defined, is a measure of closeness of analysed or planned meal (menu) to the recommendations; in other words it means an index of measure how healthy is a given meal or a menu.

Its value can be between 0 and 1, the acceptable value is PV >0.7, what is according to Wirsam and co-workers (1997) a nutritionally acceptable offer. Combinations with PV<0.7 are nutritionally unacceptable because they can have a number of adverse effects on human health, especially over a longer period of time (Wirsam & Hahn, 1999).

#### **4. Fuzzy logic based menu planning – Case study: DASH diet**

The DASH diet is considered as a case study for fuzzy logic modelling and optimisation in nutrition, considered is the DASH diet. This diet is proven as a good treatment in the prevention of height blood pressure for the high-risk population, correcting inadequate nutrition. The principles of fuzzy logic were used in the analysis and optimization process, based on developed membership functions for nutrients and food groups, for the target population of men aged 31-50 years, according to guidelines that are outlined in the treatment of hypertension (DASH guidelines: AHA, 2004).

The process of producing a quantifiable result in fuzzy logic, given fuzzy sets and corresponding membership degrees is defuzzification. This means that for every possible value *µ*, should be given a result with a grade of membership that describes to what extent this value *µ* is reasonable to use. Defuzzification is a process of transformation of this fuzzy information into a single value *µ´* that will actually be applied in the decision making process. This transformation from a fuzzy set to a crisp number (defuzzification) is

The goal, of using the fuzzy sets in nutrition is to optimize the diet so that the requirements for all observed nutrients are achieved. For example if there is too little dietary fibre and too much energy in the diet, adding wholemeal bread gives more dietary fibre but also more energy – so there is a conflict (Wirsam et al., 1997; Wirsam & Hahn, 1999; Teodorescu et al., 1999; McBride, 1997). To solve this conflict and to represent the logical "and" (because it is desirable to optimize both dietary fibre and energy), compromises are made (Wirsam & Hahn, 1999; Wirsam et al., 1999). Wirsam suggested the application of the product of the minimal membership vale and the harmonic mean to the fuzzy sets of the rest of observed nutrients, gives the name to the crisp value that defuzzifies the optimisation – the Prerow

> <sup>1</sup> min[ ] ( 1) /

μ(xi) are the fuzzy sets for *i* nutrients that are observed. So defined Prerow value is now a measure for how close on average one comes to the recommendations - or how healthy our food is. With the Prerow value one can decide whether a certain nutrition situation is better or worse than the other. Wirsam has graded the PV values (between 0 and 1) of a nutritive offer concerning their impact on health (Wirsam & Hahn, 1999; Wirsam et al., 1999). In accordance with the health impact, the preferred PV values are PV>07, and an acceptable meal or menu offer with balanced energy and nutrient offers. Those offers that result with PV > 0.9 would be considered as optimal offers with highly appreciated energy and content of nutrients. Prerow value, so defined, is a measure of closeness of analysed or planned meal (menu) to the recommendations; in other words it means an index of measure how healthy

Its value can be between 0 and 1, the acceptable value is PV >0.7, what is according to Wirsam and co-workers (1997) a nutritionally acceptable offer. Combinations with PV<0.7 are nutritionally unacceptable because they can have a number of adverse effects on human

The DASH diet is considered as a case study for fuzzy logic modelling and optimisation in nutrition, considered is the DASH diet. This diet is proven as a good treatment in the prevention of height blood pressure for the high-risk population, correcting inadequate nutrition. The principles of fuzzy logic were used in the analysis and optimization process, based on developed membership functions for nutrients and food groups, for the target population of men aged 31-50 years, according to guidelines that are outlined in the

*i*

*PV x n*

health, especially over a longer period of time (Wirsam & Hahn, 1999).

**4. Fuzzy logic based menu planning – Case study: DASH diet** 

treatment of hypertension (DASH guidelines: AHA, 2004).

*min*

*i i i*

 

*x*

(8)

*n*

necessary because humans are more familiar with crisp values.

value (PV):

is a given meal or a menu.

Basic emphasis was on nutrients whose intake, in the DASH diet, is generally important in the treatment. Emphasis was on the control of the daily intake of energy, intake of fats, saturated fats, cholesterol, magnesium, potassium, calcium, sodium, dietary fibre, proteins and carbohydrates.


\* 1,500 mg sodium was a lower goal tested and found to be even better for lowering blood pressure. It was particularly effective for middle-aged and older individuals, African Americans, and those who already had high blood pressure. g = grams; mg = milligrams

Table 1. DASH diet guideline for a 2 100 kcal Eating Plan

Fuzzy logic modelling is applied for modelling and optimisation of nutritional requirements given by DASH diet guidelines that present crisp values, as presented in table 1 where are given crisp values that should be achieved for a daily intake based on 2,100 kcal (8790 kJ) eating plan (AHA, 2004).

#### **4.1 Membership functions modelled according DASH guidelines**

In order to visualize fuzzy concept, intake of a nutrient will be estimated with a value between 0 (not belonging to the set) and 1 (completely belongs). This value of belonging to a set is defining the acceptability or unacceptability grade regarding the DASH diet.

The modelling of a fuzzy set followed the instruction of Wirsam and co-workers (1997) where 5 points are crucial in the fuzzy set construction. Those five points will be explained on the presented example for sodium intake (Figure 3). The value y is the value of the fuzzy value µ.

Five points used in the construction of the fuzzy set:


This approach in modelling of fuzzy set membership functions for the daily input was presented in some other studies what indicates the successful applicability (Wirsam & Hahn, 1999; Wirsam et al., 1997; Gajdoš et al., 2001; Rumora et al.,, 2009).

Application of Fuzzy Logic in Diet Therapy – Advantages of Application 51

The aim of the study was to use fuzzy logic in planning of the diet guidelines for people suffering from hypertension based on membership functions, for energy and nutrients of significance in the DASH diet with a balanced level of foods from different food groups. Regarding the issue of hypertension, the most vulnerable group in the population is the male population aged 31-50 years. The membership functions for energy and nutrients according to guidelines of DASH diet were developed. In the target population there are many individuals who have an inactive sedentary lifestyle, so the energy level was created

Concerning the basic aim of the DASH diet approach, the end point (5th point) of a membership function could be approximately 3 times the recommended intake for the nutrient (Wirsam et al., 1997) but this was not applied for most of the nutrients due to the

The 11 fuzzy sets for amounts of energy and nutrients most that are the most important in the DASH guidelines are constructed based on the daily energy intake of 2100 kcal and

success of a DASH diet which occurs if the recommendations are respected.

according the males with low physical activity.

according the DASH recommendations (Figure 4).

As Wirsam and co-workers (1997) have pointed out, the 5th point is "approximately 3 times the recommended intake for the nutrient". They have also advised to smooth the parabolas, what has been done in presentation of membership function presented for sodium.

Daily intake of Na concerning the crisp values that define the daily recommended intake is very simple based on equation 1: *xNa,min* ≤ *xNa* ≤ *xNa,max*, where the *xNa,min=* 500 mg, and the *xNa,max =* 2300 mg.

Fuzzy membership functions are modelled to describe the range of nutrient intakes in the range from deficient to excess amounts.

The data used in construction of fuzzy sets, as well as for the presentation of sodium intake based on crisp values are given in table 2.


(\*) Although the previous studies (Wirsam et al., 1997) have advised to use as a value for the 5th point – approximately 3 times the recommended intake for the nutrient – this was not applied, because the basic idea of the DASH diet is to reduce the intake of sodium.

Table 2. Values used in construction of membership functions (a) for normal daily intake of Na, (b) daily intake of Na based on DASH diet guidelines.

Fig. 3. Membership function, of (i) sodium as recommended by DRI and (ii) sodium according DASH guidelines and definition of the sodium daily intake based on crisp values

As Wirsam and co-workers (1997) have pointed out, the 5th point is "approximately 3 times the recommended intake for the nutrient". They have also advised to smooth the parabolas,

Daily intake of Na concerning the crisp values that define the daily recommended intake is very simple based on equation 1: *xNa,min* ≤ *xNa* ≤ *xNa,max*, where the *xNa,min=* 500 mg, and the

Fuzzy membership functions are modelled to describe the range of nutrient intakes in the

The data used in construction of fuzzy sets, as well as for the presentation of sodium intake

(\*) Although the previous studies (Wirsam et al., 1997) have advised to use as a value for the 5th point – approximately 3 times the recommended intake for the nutrient – this was not applied, because the

Table 2. Values used in construction of membership functions (a) for normal daily intake of

Fig. 3. Membership function, of (i) sodium as recommended by DRI and (ii) sodium

according DASH guidelines and definition of the sodium daily intake based on crisp values

Intake of Na according DASH diet guidelines (mg)

what has been done in presentation of membership function presented for sodium.

diet (mg)

1 0 0 0 2 0,9 500 500 3 1 1500 1000 4 0,9 2300 2000 5 0 6000 3000\*

*xNa,max =* 2300 mg.

poi

range from deficient to excess amounts.

based on crisp values are given in table 2.

nt y = µ value Intake of Na for normal

basic idea of the DASH diet is to reduce the intake of sodium.

Na, (b) daily intake of Na based on DASH diet guidelines.

The aim of the study was to use fuzzy logic in planning of the diet guidelines for people suffering from hypertension based on membership functions, for energy and nutrients of significance in the DASH diet with a balanced level of foods from different food groups. Regarding the issue of hypertension, the most vulnerable group in the population is the male population aged 31-50 years. The membership functions for energy and nutrients according to guidelines of DASH diet were developed. In the target population there are many individuals who have an inactive sedentary lifestyle, so the energy level was created according the males with low physical activity.

Concerning the basic aim of the DASH diet approach, the end point (5th point) of a membership function could be approximately 3 times the recommended intake for the nutrient (Wirsam et al., 1997) but this was not applied for most of the nutrients due to the success of a DASH diet which occurs if the recommendations are respected.

The 11 fuzzy sets for amounts of energy and nutrients most that are the most important in the DASH guidelines are constructed based on the daily energy intake of 2100 kcal and according the DASH recommendations (Figure 4).

Application of Fuzzy Logic in Diet Therapy – Advantages of Application 53

Chicken salad with Italian dressing & fruit

Chicken breast sandwich & apple juice

Beef barbeque sandwich with new potato salad & orange

Ham and cheese sandwich &carrot sticks

Tuna salad plate, canned pineapple & unsalted almonds

Turkey breast sandwich with broccoli & orange

Tuna salad sandwich, apple & low-fat

milk

Table 3. Daily offers given by AHA (2004), based on DASH diet guideline

Beef, eye of the

Unsalted almonds, raisins & fruit yogurt

Unsalted almonds, dried apricots & fruit yogurt

Fruit yogurt, graham cracker rectangles & peanut butter

Unsalted almonds, apple juice, apricots & low-fat milk

Fruit yogurt & unsalted

sunflower seeds

Unsalted peanuts, low-fat milk & dried apricots

Unsalted almonds, apple juice, dry apricots & whole wheat crackers

round

Vegetarian spaghetti & canned pears

Salad from different vegetables & cornbread muffin

Chicken with Spanish rice & low-fat milk

meatloaf, whole wheat roll & peach

Turkey

Baked fish (spicy) with cooked carrots, whole wheat roll

& cookie

salad,

Zucchini lasagne

whole wheat roll with margarine & grape juice

cocktail

 **Breakfast Lunch Dinner Snack** 

Day 1 Bran flakes cereal

with banana, low-fat milk, whole wheat

margarine & orange

whole wheat bagel with peanut butter, banana & low-fat

banana, low-fat milk whole wheat bread with margarine & orange juice

with margarine, fruit

peach & grape juice

cereal, banana, lowfat milk, raisin bagel with peanut butter &

banana, fruit yogurt, orange juice & low-fat

with banana, low-fat milk & fruit yogurt

orange juice

bread with

juice

milk

Day 3 Bran flakes cereal with

Day 4 Whole wheat bread

yogurt,

Day 5 Whole grain oat rings

Day 6 Low-fat granola bar,

milk

Day 7 whole grain oat rings

Day 2 Instant oatmeal,

Fig. 4. Membership functions for nutrients important in the DASH diet (according table 1)

#### **4.1.1 Application of membership functions of nutrients in menu evaluation**

Database of meals with nutritional content is created in Excel using the USDA database rel. 22 (USDA, 2009) based on 7 days menus taken from the official site of the American Institute of Heart, Lung and Blood (NHLBI, 2010). It is assumed that seven-day menu suggested by NHLBI according guidelines of DASH diet (Table 3) is properly conceived and would be acceptable also for pregnant women regarding the average daily energy offers ranged from 8785 – 10344 kJ. Each day offers consisted of breakfast (B), lunch (L), snack (S) and dinner (D). So, the data basis of meals was built up of 28 dishes (7 B x 7 L x 7 S x 7 D) and an ideal case result would be 2401 daily offers.

Upon creation of an eating plan for individual or group, including the person that provides the DASH eating plan, it is necessary to determine its energy and nutritional needs what is presented in table 4, for the meals given by AHA (2004).

On-line found daily offers for a weak were (i) analysed in order to evaluate the eligibility with DASH diet guidelines, and using the optimisation tool, (ii) the dish offers were combined in daily menus and (iii) new menu offers were evaluated with the corresponding PV value. In the fuzzy logic analysis, the goal is to determine the adequacy of mutual combining the individual dishes of daily meals, and to determine the number of daily combinations that are nutritionally acceptable (PV > 0.7).

The aim was to (a) analyse the daily offers and to identify the critical variables (individual nutrients), (b) optimise a set of applicable menus that are nutritive balanced.

Fig. 4. Membership functions for nutrients important in the DASH diet (according table 1)

Database of meals with nutritional content is created in Excel using the USDA database rel. 22 (USDA, 2009) based on 7 days menus taken from the official site of the American Institute of Heart, Lung and Blood (NHLBI, 2010). It is assumed that seven-day menu suggested by NHLBI according guidelines of DASH diet (Table 3) is properly conceived and would be acceptable also for pregnant women regarding the average daily energy offers ranged from 8785 – 10344 kJ. Each day offers consisted of breakfast (B), lunch (L), snack (S) and dinner (D). So, the data basis of meals was built up of 28 dishes (7 B x 7 L x 7 S x 7 D) and an ideal

Upon creation of an eating plan for individual or group, including the person that provides the DASH eating plan, it is necessary to determine its energy and nutritional needs what is

On-line found daily offers for a weak were (i) analysed in order to evaluate the eligibility with DASH diet guidelines, and using the optimisation tool, (ii) the dish offers were combined in daily menus and (iii) new menu offers were evaluated with the corresponding PV value. In the fuzzy logic analysis, the goal is to determine the adequacy of mutual combining the individual dishes of daily meals, and to determine the number of daily

The aim was to (a) analyse the daily offers and to identify the critical variables (individual

nutrients), (b) optimise a set of applicable menus that are nutritive balanced.

**4.1.1 Application of membership functions of nutrients in menu evaluation** 

case result would be 2401 daily offers.

presented in table 4, for the meals given by AHA (2004).

combinations that are nutritionally acceptable (PV > 0.7).


Table 3. Daily offers given by AHA (2004), based on DASH diet guideline

Application of Fuzzy Logic in Diet Therapy – Advantages of Application 55

assistance of Prerow features (PV value), which assesses the acceptability or unacceptability of a menu offer (a combination for a day). The combinations that resulted with a crisp value (PV value) within 0.7 to 1, was considered as acceptable daily offer, what is according to Wirsam et al. (1997) a nutritionally acceptable offer. What is the PV value closer to the value 1, the menu combination consists of nutrient amounts whose daily intake is optimal

> Guidelines for DASH diet

7 Daily offers (DO) according DASH guidelines DO = Breakfast + Lunch + Snack+ Dinner

Creating of structured data base of meals Rows: dishes Columns: 11 data about each dish (energy & 10 nutrients)

> **Fuzzification**  (a) construction of 11 fuzzy sets

> > )

**Defuzzification**  (using PV value)

(b) optimisation

Fig. 5. Flow chart of the methodology used in evaluation and optimisation of meal offers

**Planning**  of daily meal offers

During the analysis the goal was to determine the adequacy of mutual combining of individual dishes of daily meals, and to determine the number of daily combinations that are nutritionally acceptable (PV > 0.7 connotes energy and nutrient intake of all observed

nutrients in the acceptable range). Results of it are presented in table 5.

**5.1 Results of the menu analysis** 

**Analysis** of daily meal offers

(0.9<PV<1).


Table 4. Energy and nutrient content of daily offers given by AHA (2004), based on DASH diet guideline

To get an acceptable range of macro and individual entries micronutrients from existing recommendations (which represents an expression value), modelled are membership function.

Membership functions were modelled for the male population group aged 31-50, with low physical activity (PA=1), and potentially suffering from hypertension. Basic emphasis was on nutrients whose intake in the diet is general important in the treatment measures: energy, fat, saturated fat, cholesterol, magnesium, potassium, calcium, sodium, dietary fibre, proteins and carbohydrates. DASH diet guidelines emphasize the quality of fat, or fat consisting mostly n-3 and n-6 unsaturated fatty acids. Their membership functions were modelled according to their share in the total daily fat share. In addition, membership functions for individual nutrients were developed according the DASH diet guidelines.

Additionally, reviews by the American Heart Association led the Association to recommend reducing saturated fat intake to less than 7% of total calories according to its 2006 recommendations (Little et al., 2004).

The nutrient composition of the daily intake was analysed and planed following the flow chart presented on Fig. 5.

Basic guidelines for balanced energy and nutrient intake are the daily recommendations (DRI, 1990 & 2005) that define recommended daily needs of energy as well as macro and micronutrients (table 1).

#### **5. Results**

Our developed algorithm used in the daily menu analysis and optimization is written in the programming system *W.R. Mathematica v.6.*The algorithm included a feature that the solution may re-marked character (specific number) that allows decoding fuzziness, and also allows a man to understand and compare the results. Fuzziness was decoded with the

**Ed, kJ** 8800 9063 8805 9844 9362 10344 9086 8785 **Total fat , % Ed** 27 21.2 23.9 25.3 23.5 22.3 32.4 24.2 **Saturated fat , % Ed** 6 6.5 6.6 6.3 6.0 5.0 6.1 6.6 **Cholesterol , mg** 150 143.4 124.3 131.9 162.1 166.4 115.4 83.0 **Magnesium, mg** 500 529.3 428.0 609.7 535.5 558.9 579.9 545.5 **Potassium, mg** 4700 4359.5 4445.6 6124.3 4782.2 4984.9 4484.7 4147.3 **Calcium, mg** 1250 1885.3 1533.3 1487.5 1602.7 1244.1 1294.8 1443.7 **Sodium, mg** 2300 2292.3 1891.8 2115.6 2190.3 2101.5 1619.6 1714.0 **Dietary fiber, g** 30 32.0 24.7 31.1 32.6 32.3 38.0 37.7 **Protein, % Ed** 18 19.1 18.8 20.4 20.8 20.3 17.8 18.1 **Carbohydrate, % Ed** 55 59.4 57.2 54.3 55.8 57.5 49.8 57.7 Table 4. Energy and nutrient content of daily offers given by AHA (2004), based on DASH

To get an acceptable range of macro and individual entries micronutrients from existing recommendations (which represents an expression value), modelled are membership

Membership functions were modelled for the male population group aged 31-50, with low physical activity (PA=1), and potentially suffering from hypertension. Basic emphasis was on nutrients whose intake in the diet is general important in the treatment measures: energy, fat, saturated fat, cholesterol, magnesium, potassium, calcium, sodium, dietary fibre, proteins and carbohydrates. DASH diet guidelines emphasize the quality of fat, or fat consisting mostly n-3 and n-6 unsaturated fatty acids. Their membership functions were modelled according to their share in the total daily fat share. In addition, membership functions for individual nutrients were developed according the DASH diet guidelines.

Additionally, reviews by the American Heart Association led the Association to recommend reducing saturated fat intake to less than 7% of total calories according to its 2006

The nutrient composition of the daily intake was analysed and planed following the flow

Basic guidelines for balanced energy and nutrient intake are the daily recommendations (DRI, 1990 & 2005) that define recommended daily needs of energy as well as macro and

Our developed algorithm used in the daily menu analysis and optimization is written in the programming system *W.R. Mathematica v.6.*The algorithm included a feature that the solution may re-marked character (specific number) that allows decoding fuzziness, and also allows a man to understand and compare the results. Fuzziness was decoded with the

**Different daily offers Day 1 Day 2 Day 3 Day 4 Day 5 Day 6 Day 7** 

**DASH Recommendatio ns** 

**Observed** 

diet guideline

recommendations (Little et al., 2004).

chart presented on Fig. 5.

micronutrients (table 1).

**5. Results** 

function.

assistance of Prerow features (PV value), which assesses the acceptability or unacceptability of a menu offer (a combination for a day). The combinations that resulted with a crisp value (PV value) within 0.7 to 1, was considered as acceptable daily offer, what is according to Wirsam et al. (1997) a nutritionally acceptable offer. What is the PV value closer to the value 1, the menu combination consists of nutrient amounts whose daily intake is optimal (0.9<PV<1).

Fig. 5. Flow chart of the methodology used in evaluation and optimisation of meal offers

#### **5.1 Results of the menu analysis**

During the analysis the goal was to determine the adequacy of mutual combining of individual dishes of daily meals, and to determine the number of daily combinations that are nutritionally acceptable (PV > 0.7 connotes energy and nutrient intake of all observed nutrients in the acceptable range). Results of it are presented in table 5.

Application of Fuzzy Logic in Diet Therapy – Advantages of Application 57

As it was mentioned, possible number of combinations is 2041, but how many of them are acceptable (PV>0.7) based on their nutrient and energy content will show on the

> **Daily combination Prerow value (PV)**  1 B4, L4, S4, D4 0.433 2 B4, L4, S5, D4 0.477 3 B1, L1, S1, D1 0.533

> > **. . .**

. . .

Table 7. Daily offer combinations sorted according PV value (3 worst & 3 best)

2398 B3, L2, S5, D1 0.892 2399 B1, L3, S5, D2 0.893 2400 B1, L3, S1, D3 0.893 2401 B1, L2, S5, D3 0.894

A measurement of appropriate energy and nutrient intake with a respect to the recommendations, or optimal intake, is evaluated by Prerow value. PV value was used to evaluate the efficiency of meal combinations concerning the daily amount of energy and nutrients. The goal functions are optimised using originally developed program in W.R. *Mathematica* for modelling and optimisation in the Pareto sense. Sorted results, from those which are less appreciated to those that are highly recommended, have shown that 65 % are acceptable (PV>0.7), but the 35% of combinations should be avoided in the consummation

Buisson (2008) has in his study stressed out that use of fuzzy logic in meal planning results with applicable meal offers that are balanced regarding the energy and nutritive contents. Optimisation solutions provide assistance in the selection of foods and meals, and their

From the results of optimization using fuzzy logic, the proposed food guide, the DASH diet principles, can be used either for health reasons (decrease hypertension) or simply for a healthier diet. Developed software evaluates the optimal solutions considering the criterion of Prerow value, which presents the modified harmonic mean and defines a rigorous

Is there possibility that another computing approach could be more effective, can be answered only then if the same problem is solved with another tool. Fuzzy approach is placed in the nonlinear approach, so the alternative could be the linear approach, such as

The same goal (optimal daily meal offer) but solved by another tool is used in order to compare the final results and to extract advantages or disadvantages of menu planning

defuzzification (Table 7).

(Table 7).

combination with each other.

based on fuzzy logic.

criterion in the defuzzification process.

linear programming used in DASH diet planning.

**5.3 Linear programming in DASH menu planning** 

. . .


Table 5. Evaluation of daily meal combinations based on one weak DASH diet plans

As the results of the defuzzification using PV value show, not all combinations have reached the limit value of 0.7, what was an indicator of acceptance of a daily offer. Using of membership functions constructed for nutrient intake allow also identifying critical nutrient(s), as presented in the following table (Table 6).


Table 6. Analysis of the offer of day 4 with aim to detect the critical point

Experimentally determined deviations of energy and nutrients intakes from the recommendations are presented. Adjustments needed for improvement of nutrition requirements corresponding to linguistic variable were determined by use of fuzzy sets without major change of the menus.

The intake of total fats (*µ(xi)* = 0.477551) is identified as a critical nutrient. As can be seen, all other 10 observed variables *(xi)* have acceptable amounts. But because of that one critical nutrient – this daily meal combination will not be preferred.

#### **5.2 Results of the menu optimisation**

Membership functions were also used for planning new daily menu offers, based on a weekly offer that is recommended as appropriate menus for people who conducted the program according to the DASH diet principles, for 7-days (tables 3 & 4). According to the principle of modelling and optimisation (Fig. 5), the input variables (menu for 7 were evaluated using membership functions, *µ(xi)*, and estimated after the defuzzification with the crisp value PV.

Daily combination Prerow value (PV) Day 1 B1, L1, S1, D1 0.533 Day 2 B2, L2, S2, D2 0.765 Day 3 B3, L3, S3, D3 0.831 Day 4 B4, L4, S4, D4 **0.433**  Day 5 B5, L5, S5, D5 0.761 Day 6 B6, L6, S6, D6 0.818 Day 7 B7, L7, S7, D7 0.841 Table 5. Evaluation of daily meal combinations based on one weak DASH diet plans

As the results of the defuzzification using PV value show, not all combinations have reached the limit value of 0.7, what was an indicator of acceptance of a daily offer. Using of membership functions constructed for nutrient intake allow also identifying critical

> **Observed** *(xi) µ(xi)* **Amount Ed, kJ** 0.818636 9362 **Total fat , % Ed** 0.477551 23,5 **Saturated fat , % Ed** 0.905263 6,0 **Cholesterol , mg** 0.976364 162,1 **Magnesium, mg** 0.994118 535,5 **Potassium, mg** 0.900000 4782,2 **Calcium, mg** 0.909500 1602,7 **Sodium, mg** 0.837000 2190,3 **Dietary fiber, g** 0.800000 32,6 **Protein, % Ed** 0.986239 20,8 **Carbohydrate, % Ed** 0.990323 55,8

**Total PV** 0.433 Table 6. Analysis of the offer of day 4 with aim to detect the critical point

nutrient – this daily meal combination will not be preferred.

without major change of the menus.

**5.2 Results of the menu optimisation** 

Experimentally determined deviations of energy and nutrients intakes from the recommendations are presented. Adjustments needed for improvement of nutrition requirements corresponding to linguistic variable were determined by use of fuzzy sets

The intake of total fats (*µ(xi)* = 0.477551) is identified as a critical nutrient. As can be seen, all other 10 observed variables *(xi)* have acceptable amounts. But because of that one critical

Membership functions were also used for planning new daily menu offers, based on a weekly offer that is recommended as appropriate menus for people who conducted the program according to the DASH diet principles, for 7-days (tables 3 & 4). According to the principle of modelling and optimisation (Fig. 5), the input variables (menu for 7 were evaluated using membership functions, *µ(xi)*, and estimated after the defuzzification with the crisp value PV.

nutrient(s), as presented in the following table (Table 6).



Table 7. Daily offer combinations sorted according PV value (3 worst & 3 best)

A measurement of appropriate energy and nutrient intake with a respect to the recommendations, or optimal intake, is evaluated by Prerow value. PV value was used to evaluate the efficiency of meal combinations concerning the daily amount of energy and nutrients. The goal functions are optimised using originally developed program in W.R. *Mathematica* for modelling and optimisation in the Pareto sense. Sorted results, from those which are less appreciated to those that are highly recommended, have shown that 65 % are acceptable (PV>0.7), but the 35% of combinations should be avoided in the consummation (Table 7).

Buisson (2008) has in his study stressed out that use of fuzzy logic in meal planning results with applicable meal offers that are balanced regarding the energy and nutritive contents. Optimisation solutions provide assistance in the selection of foods and meals, and their combination with each other.

From the results of optimization using fuzzy logic, the proposed food guide, the DASH diet principles, can be used either for health reasons (decrease hypertension) or simply for a healthier diet. Developed software evaluates the optimal solutions considering the criterion of Prerow value, which presents the modified harmonic mean and defines a rigorous criterion in the defuzzification process.

Is there possibility that another computing approach could be more effective, can be answered only then if the same problem is solved with another tool. Fuzzy approach is placed in the nonlinear approach, so the alternative could be the linear approach, such as linear programming used in DASH diet planning.

#### **5.3 Linear programming in DASH menu planning**

The same goal (optimal daily meal offer) but solved by another tool is used in order to compare the final results and to extract advantages or disadvantages of menu planning based on fuzzy logic.

Application of Fuzzy Logic in Diet Therapy – Advantages of Application 59

 *Sj + aij .*

 *Sj + aij .*

 *Dj ≥ bi, min* (11)

 *Dj ≤ bi, max* (12)

 *Lj + aij .*

 *Lj + aij .*

**aij**- Content of energy, water or nutrients, i, i=1, 2, . . ., 20, for observed meals, j

In order to construct a linear models as similar as possible to the fuzzy model, the price of all offers was set equal to one, what would allow to optimise without of price influence (because the price was not included in the meal planning based on fuzzy logic). Program

Each daily offer included the same offer as in the previous example: one breakfast (B), lunch (L), snack (S) and dinner (D). Again, the data basis of meals was built up of 28 dishes (7 B x 7 L x 7 S x 7 D) and an ideal case result would be 2401 daily offers. But using the optimisation tools, it will be cleared if all combinations (daily offers) are well balanced concerning the required energy and nutrient content. The aim was also to examine whether the target group will satisfy all energy and nutrient needs, without additional changes of the offers,

> Daily meal offer, LP No. 1 B1, L2, S5, D1 No. 2 B2, L2, S1, D2 No. 3 B1, L2, S1, D7 No. 4 B7, L3, S2, D1 No. 5 B1, L1, S2, D5

The nutrient compositions of daily intakes were based on restrictions selected with respect to the target group of men aged 31-50 with the emphasis to sedentary job. Based on the composition, weekly plan have been proposed that consisted of 7meals distributed during the day as breakfast, lunch, snack and dinner (Table 9). The average values of energy and nutrients of the offers can, without problems, composed menu offers for almost 2 months (even 63 daily offers satisfied all demands on energy and nutrients).The present study combines the limitations of menu offers (NHLBI, 2010) and of modelling approaches. In particular, the validity of results obtained with diet modelling analysis is dependent on how

In order to identify the critical variables (individual meals) or constrains (nutrient requirements), the sensitivity test was used (Gajdoš et al., 2001). But collection of those result are much more demanding because each new solution requires repetition performance of the optimisation process. Until now, it has been used to design either

Table 9. First five daily offers as a result of using linear optimisation tools

well the models simulate reality and on the quality of input data.

Constrains that will restrict energy and nutrient content of daily offers:

 *Bj + aij .*

 *Bj + aij .*

*aij .*

*aij .*

**bi** - Recommended intakes of energy, water or nutrients

**xj** - Meals, number of the meals (j), j=1, ... , 7

LINDO was used as linear optimisation program.

Where:

**pj** - Meal price

through menu offers.

Linear programming is designed to address the problem by choosing between several possible or available variables in order to achieve the most suitable combination of the selected (optimal) result (Kalpić and Mornar, 1996; Deb, 2001, Darmon et al, 2002). Applying these premises (goal and constrains), models were constructed in order to find the so called – optimal solution. Models containing such target function and a set of admissible constrains are called linear models (Eckstein, 1967; Martić, 1996; Kalpić and Mornar, 1996) and are often used in menu planning (Gajdoš et al., 2001; Koroušić Seljak, 2009). Using linear optimisation in menu planning, it is very important to indicate the upper and lower limits, i.e. minimum and/or maximum value that is needed to satisfy the daily nutrition needs (Bhatti, 2000):

#### **Minimum** ≤ **acceptable nutrient amounts** ≤ **Maximum** (9)

Nutrient needs are often defined in ranges as mentioned in eq. 1) what will be in detail explained in materials and methods (especially in table 2 and figure 1).

According to the target group, males aged 30-51, it was important, from a set of data, choose those items that are crucial for the DASH diet (Table 8).


\*the range of the minimum and maximal value is ± 10% of the recommended value

Table 8. Recommended intake of energy and macronutrients according DAH guidelines and their limitations used in meal planning using linear programming

The aim is to reach a result that presents a daily energy and nutritive balanced offer with minimal cost. Price was placed in the aim function of the linear model where energy and 10 nutrients (total Proteins, Fats, Carbohydrates, Saturated Fats Dietary Fibres, Cholesterol, Calcium, Magnesium, Sodium and Potassium) were included in the constrains subjected to the goal function, as follows in the basic linear model.

Basic structure of the linear model:

Goal function:

$$\min \text{F=} \mathbf{p}\_1 \mathbf{B}\_1 + \dots + \mathbf{p}\_7 \mathbf{B}\_7 + \mathbf{p}\_8 \mathbf{L}\_1 + \dots + \mathbf{p}\_{14} \mathbf{L}\_7 + \mathbf{p}\_{15} \mathbf{S}\_1 + \dots + \mathbf{p}\_{21} \mathbf{S}\_7 + \mathbf{p}\_{22} \mathbf{D}\_1 + \dots + \mathbf{p}\_{28} \mathbf{D}\_7 \tag{10}$$

Constrains that will restrict energy and nutrient content of daily offers:

$$a\_{i\uparrow} \cdot B\_{\uparrow} + a\_{i\downarrow} \cdot L\_{\uparrow} + a\_{i\downarrow} \cdot S\_{\uparrow} + a\_{i\downarrow} \cdot D\_{\downarrow} \cong b\_{i,\text{min}}\tag{11}$$

$$a\_{\rm ii} \cdot B\_{\rm j} + \,\, a\_{\rm ii} \cdot L\_{\rm j} + a\_{\rm ii} \cdot S\_{\rm j} + a\_{\rm ii} \cdot D\_{\rm j} \le b\_{\rm i, \max} \tag{12}$$

Where:

58 Fuzzy Logic – Emerging Technologies and Applications

Linear programming is designed to address the problem by choosing between several possible or available variables in order to achieve the most suitable combination of the selected (optimal) result (Kalpić and Mornar, 1996; Deb, 2001, Darmon et al, 2002). Applying these premises (goal and constrains), models were constructed in order to find the so called – optimal solution. Models containing such target function and a set of admissible constrains are called linear models (Eckstein, 1967; Martić, 1996; Kalpić and Mornar, 1996) and are often used in menu planning (Gajdoš et al., 2001; Koroušić Seljak, 2009). Using linear optimisation in menu planning, it is very important to indicate the upper and lower limits, i.e. minimum and/or maximum value that is needed to satisfy the daily nutrition needs

 **Minimum** ≤ **acceptable nutrient amounts** ≤ **Maximum** (9) Nutrient needs are often defined in ranges as mentioned in eq. 1) what will be in detail

According to the target group, males aged 30-51, it was important, from a set of data, choose

Ed, kJ **8800** 8000 9600 Total fat , % Ed **27** 24.3 29.7 Saturated fat , % Ed **6** 5.4 6.6 Cholesterol , mg **150** 135 165 Magnesium, mg **500** 450 550 Potassium, mg **4700** 4230 5170 Calcium, mg **1250** 1125 1375 Sodium, mg **2300** 2070 2530 Dietary fiber, g **30** 27 33 Protein, % Ed **18** 16.2 19.8 Carbohydrate, % Ed **55** 50 60

*Daily recommendations\* used for LP*  **Minimum Minimum** 

explained in materials and methods (especially in table 2 and figure 1).

**Recommendations** 

\*the range of the minimum and maximal value is ± 10% of the recommended value

L1 + ... + p14.

their limitations used in meal planning using linear programming

the goal function, as follows in the basic linear model.

B7 + p8.

Basic structure of the linear model:

B1 + ... + p7.

Goal function:

min F= p1.

Table 8. Recommended intake of energy and macronutrients according DAH guidelines and

The aim is to reach a result that presents a daily energy and nutritive balanced offer with minimal cost. Price was placed in the aim function of the linear model where energy and 10 nutrients (total Proteins, Fats, Carbohydrates, Saturated Fats Dietary Fibres, Cholesterol, Calcium, Magnesium, Sodium and Potassium) were included in the constrains subjected to

L7 + p15.

S1 + ... + p21.

S7 + p22.

D1 + ... + p28.

D7 (10)

those items that are crucial for the DASH diet (Table 8).

Observed **DASH** 

(Bhatti, 2000):


**xj** - Meals, number of the meals (j), j=1, ... , 7

**aij**- Content of energy, water or nutrients, i, i=1, 2, . . ., 20, for observed meals, j

**bi** - Recommended intakes of energy, water or nutrients

In order to construct a linear models as similar as possible to the fuzzy model, the price of all offers was set equal to one, what would allow to optimise without of price influence (because the price was not included in the meal planning based on fuzzy logic). Program LINDO was used as linear optimisation program.

Each daily offer included the same offer as in the previous example: one breakfast (B), lunch (L), snack (S) and dinner (D). Again, the data basis of meals was built up of 28 dishes (7 B x 7 L x 7 S x 7 D) and an ideal case result would be 2401 daily offers. But using the optimisation tools, it will be cleared if all combinations (daily offers) are well balanced concerning the required energy and nutrient content. The aim was also to examine whether the target group will satisfy all energy and nutrient needs, without additional changes of the offers, through menu offers.


Table 9. First five daily offers as a result of using linear optimisation tools

The nutrient compositions of daily intakes were based on restrictions selected with respect to the target group of men aged 31-50 with the emphasis to sedentary job. Based on the composition, weekly plan have been proposed that consisted of 7meals distributed during the day as breakfast, lunch, snack and dinner (Table 9). The average values of energy and nutrients of the offers can, without problems, composed menu offers for almost 2 months (even 63 daily offers satisfied all demands on energy and nutrients).The present study combines the limitations of menu offers (NHLBI, 2010) and of modelling approaches. In particular, the validity of results obtained with diet modelling analysis is dependent on how well the models simulate reality and on the quality of input data.

In order to identify the critical variables (individual meals) or constrains (nutrient requirements), the sensitivity test was used (Gajdoš et al., 2001). But collection of those result are much more demanding because each new solution requires repetition performance of the optimisation process. Until now, it has been used to design either

Application of Fuzzy Logic in Diet Therapy – Advantages of Application 61

But the great advantage of using fuzzy arithmetic in menu planning is the suitability to deal with the inherent imprecision of data associated with nutrient values. The fuzzification and defuzzification process are a great help in achievement of analysis or balanced menu offers. In the future research, new variables will be added to the set of membership functions of energy and nutrients. Those two variables are (i) preferences of the consumer and (ii) the price of a daily menu combination. The following aim is to balance the menu offers globally, including all mentioned membership functions (11 presented in this chapter + 2 new:

Before the construction of the membership function for the consumer preference, it is necessary to carry out the evaluation of the offers, i.e. of each meal (Breakfast, Lunch, Dinner and Snack). The evaluative scale can be arbitrary, for example, if the Likert-type scale from 1 to 5 is used, the values used in the construction of the curve should be as following: 1 - "totally unacceptable", 2 - "not acceptable" 3 - "moderately acceptable" , 4 - "acceptable", 5 - "very acceptable". Membership function that describes the preference of the consumer will have the shape "S" (Fig. 2, *µ(A1)*), because for the consumer is not acceptable to consume something that is not preferable. The membership function of acceptability (consumers preference) can also be used to exclude any food ingredient that is a potential allergen (a meal that contains any allergen is "totally unacceptable"). Allergens that could be removed in such menu planning are milk, eggs, nuts, grains, etc. Each offer that contain allergens would be unacceptable (μ(x) <0.5) and according the equation 8., the final PV

Membership function for the price (daily price acceptance) of the daily menu offer should have the form "Z" (Fig. 2, *µ(A2)*), because user-friendly is the lower price (μ(x) > 0.7), although daily offers that are expensive should not be excluded because such offer can be

This software should be also used in education of users (either healthy or sick) to enlarge their knowledge regarding food combining and menu planning. Efficient education based on the software that is based on using fuzzy logic, intended for nutrient intake analysis and/or planning, would be a powerful tool in the fight with the growing world problem – obesity.

Alderman, M. H. (1999). Barriers to blood pressure control. *American Journal of Hypertension*,

American Heart Association (AHA) (2004). Heart disease and stroke statistics—2004 update.

Association Available: http://www.americanheart.org/presenter.jhtml?identifier= 1928.

Appel, L. J.; Moore, T. J.; Obarzanek, E.; Vollmer, W. M.; Svetkey, L. P. & Sacks, F. M. (1997).

Bingham, S.A. (1987). The dietary assessment of individuals; methods, accuracy, new

A clinical trial of the effects of dietary patterns on blood pressure. *The New England* 

techniques and recommendations. *Nutrition Abstracts and Reviews*, Vol. 57, No. 9,

Vol.12, (December, 1999) pp. 1268–1269, ISSN 0895-7061

Dallas, TX7 American Heart

Accessed December 6, 2004.

pp. 705-742, ISSN 0029-6019

*Journal of Medicine*, 336, 1117–1124.

preference and price).

value would not be acceptable.

nutritionally very acceptable.

**7. References** 

individual diets (Soden and Fletcher, 1992; Colavita and D`Orsi, 1990) or population diets (Maes et al., 2008; Carlson et al., 2007; Cleveland et al., 1993; Darmon et al., 2002) and their implications in terms of food choices (Ferguson et al., 2006).

As some studies show (Carlson et al., 2007; Murphy and Britten, 2006; Katamay et al., 2007; Cleveland et al., 1993; Soden and Fletcher, 1992) the main goal of linear programming used in meal planning is to reach the nutrient-based recommendations and also translation of the set of nutrient-based recommendations into foods (not food composites) for each individual or group that is a representative sample of the target population (Maillot et al., 2010), that are in accordance with set limits and the goal function.

#### **6. Conclusion**

The menu planning based on fuzzy logic considered and including: i) recommendations as crisp values, ii) modelling of membership functions for daily energy and nutrient intake as well as for preferences and price (Pareto optimisation), iii) defuzzification and iv) identification of deviations in order to improve the daily intake.

The final result of the optimisation process was a set of daily menus, 65% of which are nutritional acceptable. The acceptable daily combinations can be used in healthy meal planning and in prevention and treatment of hypertension, changing nutritional habits according DASH guidelines. This would also help to avoid consumption of unacceptable daily offers (almost 35%) from the set.

The use of fuzzy logic has also highlighted the possibility of insufficient energy and nutrient intake when dishes from different daily offers are combined in an inadequate way.

Using optimisation in meal planning showed that the energy amount in the optimised meals is in proportion with DASH recommendations with no fear of the influence on health, as Wirsam and Hahn (1999) pointed out.

The results indicated that use of fuzzy logic is well suited to deal with the inherent imprecision of data associated with food quantities and their nutrient values, and to propagate it through computations in a mathematical way with a great applicability in diet planning as well as in the demanding cases as DASH diet planning.

From one weekly offer undertaken from NHLBI (2010) that is consisted from 7 daily offers based on 4 dishes (breakfast, lunch, snacks, and dinner) was possible to gain 2401 daily offers but using the optimisation approach it was shown that it is not possible to combine all dishes in new a daily offers because the nutrient composition will not satisfy needs of the target group, man aged 30-51 with the emphasis to hypertension.

From possible 2401 daily offers (new daily menus) the final menu set was reduced on 63 daily offers, almost 2 months. Each weekly plan that has been proposed consisted of 4 meals distributed during the day as breakfast, lunch, snack and dinner. This indicates the limitation of the optimisation approach regarding the input data set, the weekly offer undertaken from NHLBI (2010). This example has shown that when the importance of the objective function is reduced (equal for all offers), this is a deficiency of the LP in meal planning and is no competition at all to the application of fuzzy logic in meal planning.

But the great advantage of using fuzzy arithmetic in menu planning is the suitability to deal with the inherent imprecision of data associated with nutrient values. The fuzzification and defuzzification process are a great help in achievement of analysis or balanced menu offers.

In the future research, new variables will be added to the set of membership functions of energy and nutrients. Those two variables are (i) preferences of the consumer and (ii) the price of a daily menu combination. The following aim is to balance the menu offers globally, including all mentioned membership functions (11 presented in this chapter + 2 new: preference and price).

Before the construction of the membership function for the consumer preference, it is necessary to carry out the evaluation of the offers, i.e. of each meal (Breakfast, Lunch, Dinner and Snack). The evaluative scale can be arbitrary, for example, if the Likert-type scale from 1 to 5 is used, the values used in the construction of the curve should be as following: 1 - "totally unacceptable", 2 - "not acceptable" 3 - "moderately acceptable" , 4 - "acceptable", 5 - "very acceptable". Membership function that describes the preference of the consumer will have the shape "S" (Fig. 2, *µ(A1)*), because for the consumer is not acceptable to consume something that is not preferable. The membership function of acceptability (consumers preference) can also be used to exclude any food ingredient that is a potential allergen (a meal that contains any allergen is "totally unacceptable"). Allergens that could be removed in such menu planning are milk, eggs, nuts, grains, etc. Each offer that contain allergens would be unacceptable (μ(x) <0.5) and according the equation 8., the final PV value would not be acceptable.

Membership function for the price (daily price acceptance) of the daily menu offer should have the form "Z" (Fig. 2, *µ(A2)*), because user-friendly is the lower price (μ(x) > 0.7), although daily offers that are expensive should not be excluded because such offer can be nutritionally very acceptable.

This software should be also used in education of users (either healthy or sick) to enlarge their knowledge regarding food combining and menu planning. Efficient education based on the software that is based on using fuzzy logic, intended for nutrient intake analysis and/or planning, would be a powerful tool in the fight with the growing world problem – obesity.

#### **7. References**

60 Fuzzy Logic – Emerging Technologies and Applications

individual diets (Soden and Fletcher, 1992; Colavita and D`Orsi, 1990) or population diets (Maes et al., 2008; Carlson et al., 2007; Cleveland et al., 1993; Darmon et al., 2002) and their

As some studies show (Carlson et al., 2007; Murphy and Britten, 2006; Katamay et al., 2007; Cleveland et al., 1993; Soden and Fletcher, 1992) the main goal of linear programming used in meal planning is to reach the nutrient-based recommendations and also translation of the set of nutrient-based recommendations into foods (not food composites) for each individual or group that is a representative sample of the target population (Maillot et al., 2010), that

The menu planning based on fuzzy logic considered and including: i) recommendations as crisp values, ii) modelling of membership functions for daily energy and nutrient intake as well as for preferences and price (Pareto optimisation), iii) defuzzification and iv)

The final result of the optimisation process was a set of daily menus, 65% of which are nutritional acceptable. The acceptable daily combinations can be used in healthy meal planning and in prevention and treatment of hypertension, changing nutritional habits according DASH guidelines. This would also help to avoid consumption of unacceptable

The use of fuzzy logic has also highlighted the possibility of insufficient energy and nutrient

Using optimisation in meal planning showed that the energy amount in the optimised meals is in proportion with DASH recommendations with no fear of the influence on health, as

The results indicated that use of fuzzy logic is well suited to deal with the inherent imprecision of data associated with food quantities and their nutrient values, and to propagate it through computations in a mathematical way with a great applicability in diet

From one weekly offer undertaken from NHLBI (2010) that is consisted from 7 daily offers based on 4 dishes (breakfast, lunch, snacks, and dinner) was possible to gain 2401 daily offers but using the optimisation approach it was shown that it is not possible to combine all dishes in new a daily offers because the nutrient composition will not satisfy needs of the

From possible 2401 daily offers (new daily menus) the final menu set was reduced on 63 daily offers, almost 2 months. Each weekly plan that has been proposed consisted of 4 meals distributed during the day as breakfast, lunch, snack and dinner. This indicates the limitation of the optimisation approach regarding the input data set, the weekly offer undertaken from NHLBI (2010). This example has shown that when the importance of the objective function is reduced (equal for all offers), this is a deficiency of the LP in meal planning and is no competition at all to the application of fuzzy logic in meal planning.

intake when dishes from different daily offers are combined in an inadequate way.

implications in terms of food choices (Ferguson et al., 2006).

are in accordance with set limits and the goal function.

daily offers (almost 35%) from the set.

Wirsam and Hahn (1999) pointed out.

identification of deviations in order to improve the daily intake.

planning as well as in the demanding cases as DASH diet planning.

target group, man aged 30-51 with the emphasis to hypertension.

**6. Conclusion** 


Application of Fuzzy Logic in Diet Therapy – Advantages of Application 63

Hahn, P.; Pfeiffenberger, P.; Wirsam, B. & Leitzmann, C. (1995a). Bewertung und

Hajjar, I. & Kotchen, T. A. (2003). Trends in prevalence, awareness, treatment, and control of

intake pattern, *Nutrition Reviews*, Vol.65, No4, pp. 155–166, ISSN 1753-4887 Klir, G.J.; Clair, U.S. & Yuan, B. (1997). *Fuzzy set theory – foundations and applications*. Prentice-

Koroušić Seljak B. (2009): Computer-based dietary menu planning, *Journal of Food* 

Kumanyika, S. K. (1997). Can hypertension be prevented? Applications of risk modifications

Lehmann, I.; Weber, R. & Zimmermann, H.J. (1992) Fuzzy Set Theory. *OR Spektrum* Vol.14,

Maes, L.; Vereecken, C.A.; Gedrich, K..; Rieken, K.; Sichert-Hellert, W.; De Bourdeaudhuij, I.;

Leventhal, H.; Diefenbach, M., & Leventhal, E. A. (1992). Illness cognition: Using common

*Therapy and Research*, Vol.16, No.2, (March, 1992) pp. 143–163, ISSN: 143-163 Little, P.; Kelly, J.; Barnett J.; Dorward, M.; Margetts, B., & Warm, D. (2004). Randomised

MacMahon, S. & Rogers, A. (1993). The effects of blood pressure reduction in older patients:

McCarron, D. A. (1998). Diet and blood pressure—The paradigm shift. *Science*, Vol.281,

Mahan K. L. & Escott-Stump S. (2007). *Krause's Food and Nutrition Therapy,* 12ed, ISBN 978-1-

Maillot M.; Vieux F.; Amiot M.J. & Darmon N. (2010). Individual diet modelling translates

Martić Lj. (1996) *Matematičke metode za ekonomske analize,* ISBN 067614-787-X, Školska knjiga,

No.5379, (August, 1998), pp. 933–934, ISSN: 1095-9203

4160-3401-8, Saundres, Elsevier, Philadelphia,

*Composition and Analysis*, Vol.22, No5, pp. 414-420, ISSN 0889-1575

*Association*, Vol.290, No.2, (July, 2003), 199– 206, ISSN: 0025-6196 Kalpić D. & Mornar V. (1996). *Operacijska istraživanja*, ISBN 9536363070, DRIP, Zagreb. Katamay S.W.; Esslinger K.A.; Vigneault M.; Johnston J.L.; Junkins B.A.; Robbins L.G.; Sirois

Vol.42, pp. 367-371, ISSN 0174-0008

Hall, Inc., London.

New York, Springer.

ISSN 0307-0565

2004), pp.1054.

ISSN 0002-9165

Zagreb.

1554-2815

No.1, pp. 1-9, ISSN 0171-6468

Optimierung der Nährstoffzufuhr mit Hilfe der Fuzzy-Logik. *Ernährungs-Umschau,*

hypertension in the United States, 1988–2000. *Journal of the American Medical* 

I.V.; Jones-McLean E.M.; Kennedy A.F.; Bush M.A.A.; Brulé D. & Martineau C. (2007). Eating well with Canada's Food Guide (2007): development of the food

in Black populations: U.S. populations. *Proceedings of the Eleventh International Interdisciplinary Conference on Hypertension in Blacks*. (p. 72–77). New Orleans, LA:

Kersting, M.; Manios, Y.; Plada, M.; Hagströmer, M.; Dietrich, S. & Matthys. C. on behalf of the HELENA Study Group (2008). A feasibility study of using a diet optimization approach in a web-based computer-tailoring intervention for adolescents, *International Journal of Obesity,* Vol.32, No.S5, (May, 2008), pp.S76–S81,

sense to understand treatment adherence and affect cognition interactions. *Cognitive* 

controlled factorial trial of dietary advice for patients with a single high blood pressure reading in primary care. *British Medical Journal*, Vol.328, No.7447, (May,

An overview of five randomized controlled trials in elderly hypertensives. *Clinical and Experimental Hypertension*, Vol.15, No.6, (November, 1993), pp. 967–968, ISSN:

nutrient recommendations into realistic and individual-specific food choices, *American Journal of Clinical Nutrition,* Vol.91, No.2, (November, 2009) pp. 421-430,


Brown, M.L.; Filer, L.J.; Guthrie, H.A.; Levander, O.A.; McComick, D.B.; Olson, R.E. &

Buisson, J-C. (2008). Nutri-Educ, a nutrition software application for balancing meals, using

Burt, V. L.; Whelton, P.; Roccella, E. J.; Brown, C.; Cutler, J. A. & Higgins, M. (1995).

Carlson, A.; Lino M. & Fungwe T. (2007). The low-cost, moderate-cost, and liberal food

Cook, N. R.; Cohen, J.; Hebert, P. R.; Taylor, J. O. & Hennekens, C. H. (1995). Implications of

Čerić, V. & Dalbelo-Bašić, B. (2004). *Informacijska tehnologija u poslovanju*, ISBN: 953-197-640-

Dantzig G.B. (1990). The diet problem, *Interfaces,* Vol.20, No.4, (July/August 1990), pp. 43–

Darmon N.; Ferguson E. & Briend A. (2002). Linear and nonlinear programming to optimize

Deb K. (2001). *Multi-Objective Optimization Using Evolutionary Algorithms*, ISBN 0471 87339 X,

Dietary Reference Intakes (1999). A Risk Assessment Model for Establishing Upper Intake

Dietary Reference Intakes (2001). Intake of Calcium, Phosphorus, Magnesium, Vitamin D and Fluoride. National Academy Press, Washington, D.C., ISBN 0-309-06403-1 Dietary Reference Intakes (2001a) Intakes for Vitamin A, Vitamin K, Arsenic, Boron,

Dietary Reference Intakes(2001b) Applications in Dietary Assessment: A Report of the

Ferguson E.L.; Darmon N.; Fahmida U.; Fitriyanti S.; Harper T.B. & Premachandra I.M.

*Nutrition*, Vol.136, No.9, (September, 2006), pp. 2399–2404, ISSN 0022-3166 Gajdoš J.; Vidaček S. & Kurtanjek Ž. (2001). Meal planning in boarding schools in Croatia

Hahn, A.; Pfeifenberger, P. & Wirsam, B. (1995). Evaluation and optimisation of nutrient supply by fuzzy-logic. *Ernahrungs-Umschau,* Vol.42, pp. 367, ISSN 0174-0008

Levels for Nutrients, Institute of Medicine. ISBN 0-309-07520-3

Life Science Institute Nutrition Foundation Washington D.C.

Vol.25, No.3, (March, 1995), pp. 305–313, ISSN 1524-4563

*Internal Medicine*, Vo.155. No.7, (November, 1995), pp. 701–709.

(February, 2002) pp. 245–253, ISSN 0002-9165

Vol.42, pp. 213-227, ISSN 0933-3657.

and Promotion (CNPP-20.)

6, Element, Zagreb.

47, ISSN 0092-2102

John Wiley & Sons, Ltd.

Medicine. ISBN 0-309-07183-6

*Environment*, 2, (February, 2001), pp. 217-222.

07279-4

Steele, R.D. (1990). *Present Knowledge in Nutrition*, ISBN 1578811074, International

fuzzy arithmetic and heuristic search algorithms, *Artificial Intelligence in Medicine,*

Prevalence of hypertension in the US adult population: Results from the Third National Health and Nutrition Examination Survey, 1988–1991*. Hypertension*,

plans. Washington, DC: US Department of Agriculture, Center for Nutrition Policy

small reductions in diastolic blood pressure for primary prevention. *Archives of* 

the nutrient density of a population's diet: an example based on diets of preschool children in rural Malawi, *American Journal of Clinical Nutrition*, Vol.75, No.2,

Chromium, Copper, Iodine, Iron, Manganese, Molybdenum, Nickel, Silicon, Vanadium, and Zinc, Food and Nutrition Board, Institute of Medicine, ISBN 0-309-

Subcommittees on Interpretation and Uses of Dietary Reference Intakes and Upper Reference Levels of Nutrients, and the Standing Committee on the Scientific Evaluation of Dietary Reference Intakes, Food and Nutrition Board, Institute of

(2006). Design of optimal food-based complementary feeding recommendations and identification of key "problem nutrients" using goal programming, *Journal of* 

using optimisation of food components. *Current Studies of Biotechnology –* 


**4** 

 *Italy* 

**Fuzzy Logic and Neuro-Fuzzy Networks for** 

Pollution and management of the environment are serious problems which concern the entire planet; the main responsibility should be attributed to human activities that contribute significantly to damage the environment, leading to an imbalance of natural ecosystems. In recent years, numerous studies focused on the three environmental compartments: soil, water and air. The pollution of groundwater is a widespread problem. The causes of pollution are often linked to human activities, including waste disposal.

Solid waste management has become an important environmental issue in industrialized countries. The most serious problems are related to solid waste disposal. Landfill is still the most used disposal technique but not the safest. In fact, a breakdown of containment elements could easily occur even in controlled landfills. This breakdown could cause contamination of aquifer that is environmental pollution. Such contamination can be mitigated by performing remediation and environmental restoration. The assessment of environmental pollution risk can be performed with different degrees of detail and

Various statistical and mathematical models can be used for a qualitative risk assessment. The planning of a program for environmental remediation and restoration can be supported by expeditious methodologies that allow us to obtain a hierarchical classification of contaminated sites. The literature offers some expeditious and qualitative methods including fuzzy logic (Zadeh, 1965), neural networks and neuro-fuzzy networks, which are more objective methods. The three artificial intelligence systems differ among themselves in some respects: fuzzy inference system learns knowledge of data only through the fuzzy rules; neural network is able to learn knowledge of data using the weights of synaptic connections; neuro-fuzzy systems are able to learn knowledge of neural data with neural

Fuzzy logic was founded in 1965 by Zadeh. The first applications date back to the nineties. They were mainly used to control industrial processes, household electrical appliances and means of transport. Later, this approach was used in several fields including the

paradigm and represent it in the form of fuzzy rules.

**1. Introduction** 

precision.

**Environmental Hazard Assessment** 

*Department of Engineering and Physics of the Environment,* 

Ignazio M. Mancini, Salvatore Masi, Donatella Caniani and Donata S. Lioi

 *University of Basilicata,* 


### **Fuzzy Logic and Neuro-Fuzzy Networks for Environmental Hazard Assessment**

Ignazio M. Mancini, Salvatore Masi, Donatella Caniani and Donata S. Lioi *Department of Engineering and Physics of the Environment, University of Basilicata, Italy* 

#### **1. Introduction**

64 Fuzzy Logic – Emerging Technologies and Applications

hlbi.nih.gov/health/public/ heart/hbp/dash/week\_dash.html>. Accessed 25th

Novák, V. (2005). Are fuzzy sets a reasonable tool for modeling vague phenomena?, *Fuzzy Sets and Systems* Vol.156, No.3, (January 2005), pp.341—348, ISSN 0165-0114 Novák, V.; Perfilieva, I. & Močkoř, J. (1999). *Mathematical principles of fuzzy logic* ISBN 0-7923-

Ray, T.; Liew, K. M. & Saini, P. (2002). An intelligent information sharing strategy within a

Rödder, W. & Zimmermann, H.J. (1977). Analyse, Beschreibung und Optimirung von

Rumora, I.; Gajdoš Kljusurić, J. & Bosanac, V. (2009). Analysis and optimisation of calcium

Soden P.M. & Fletcher L.R. (1992). Modifying diets to satisfy nutritional requirements using

Siri-Tarino PW, Sun Q, Hu FB, Krauss RM (2010). "Saturated fat, carbohydrate, and

Stachowicz, M.S. and Beall, L. (1995). *Manual for Software Mathematica-Notebook*, Wolfram

Teodorescu, H-N., Kandel, A., Jain, L.C. (1999). Soft *Computing in Human-Related Sciences*,

Wirsam, B., Hahn, A. (1999). Fuzzy methods in nutrition planning and education and

USDA, US Department of Agriculture (2009) USDA National Nutrient Database for

Wirsam, B., Hahn, A., Uthus, E.O., Leitzmann, C. (1997). Aplication of fuzzy methods for

International Union of Nutrition Sciences, Montreal, July/August 1997 Wirsam, B.; Hahn, A.; Uthus, E.O. & Leitzmann, C. (1997a). Fuzzy sets and fuzzy decision

Zadech, L.A. (1965). Fuzzy Sets. *Information and Control* Vol.8, pp. 338-353, ISSN 1349-4198 Zadech, L. A. (1996). *Fuzzy Sets, Fuzzy Logic, Fuzzy Systems*, ISBN 9810224214, World

Zadech, L.A. (1994). The role of fuzzy logic in modelling, identification and control. *Modelling Identification & Control*. Vol.15, No.3, pp. 191-203, ISSB 1890-1328. Zadech, L.A. (1997). Toward a theory of fuzzy information granulation and its centrality in

Zadech, L.A. (2001) A new direction in AI- Toward a computational theory of perceptions.

*AI Magazine*, Vol.22, No.19, pp. 73-84, ISSN 0738-4602

swarm for unconstrained and constrained optimisation problems*. Soft Computing*

unscarf formulierten Problemen. *Zeitschrift für Operations Research*, Vol.21, pp. 1-18,

content in menus and dairy offer in Croatian kindergartens. *Mljekarstvo*, Vol.59,

linear programming, *British Journal of Nutrition,* Vol.68, No.3, (December, 1991), pp.

cardiovascular disease". The American Journal of Clinical Nutrition, Vol.91, No.3,

clinical nutrition, in Soft Computing in human-related sciences, ISBN 0849316359,

setting RDA's. Poster at the 16th International Congress of Nutrition by the

making in nutrition. European Journal of Clinical Nutrition, Vol.51, No.5, (May,

Human Reasoning and Fuzzy logic. *Fuzzy Sets & Systems*, Vol.90, No.2, pp. 111-127,

NHLBI (2010). National Hart Lung and Blood Institute <http://www.n

No.3, (November, 2009), pp. 201-208, ISSN 0026-704X

(March, 2010), pp. 502–509, ISSN 1938-3207

ISBN 0849316359, CRC Press. New York,

8595-0, Dodrecht: Kluwer Academic.

Vol.6, No.1, pp. 38-34, ISSN 1432-7643

March 2010.

ISSN 0340-9422

565–572, ISSN 0007-1145

CRC Press, Florida.

Scientific Press.

ISSN: 0165-0114

Research, Champaign, Illinois.

Standard Reference, Release 22.

1997), pp. 286-296, ISSN: 0954-3007

Pollution and management of the environment are serious problems which concern the entire planet; the main responsibility should be attributed to human activities that contribute significantly to damage the environment, leading to an imbalance of natural ecosystems. In recent years, numerous studies focused on the three environmental compartments: soil, water and air. The pollution of groundwater is a widespread problem. The causes of pollution are often linked to human activities, including waste disposal.

Solid waste management has become an important environmental issue in industrialized countries. The most serious problems are related to solid waste disposal. Landfill is still the most used disposal technique but not the safest. In fact, a breakdown of containment elements could easily occur even in controlled landfills. This breakdown could cause contamination of aquifer that is environmental pollution. Such contamination can be mitigated by performing remediation and environmental restoration. The assessment of environmental pollution risk can be performed with different degrees of detail and precision.

Various statistical and mathematical models can be used for a qualitative risk assessment. The planning of a program for environmental remediation and restoration can be supported by expeditious methodologies that allow us to obtain a hierarchical classification of contaminated sites. The literature offers some expeditious and qualitative methods including fuzzy logic (Zadeh, 1965), neural networks and neuro-fuzzy networks, which are more objective methods. The three artificial intelligence systems differ among themselves in some respects: fuzzy inference system learns knowledge of data only through the fuzzy rules; neural network is able to learn knowledge of data using the weights of synaptic connections; neuro-fuzzy systems are able to learn knowledge of neural data with neural paradigm and represent it in the form of fuzzy rules.

Fuzzy logic was founded in 1965 by Zadeh. The first applications date back to the nineties. They were mainly used to control industrial processes, household electrical appliances and means of transport. Later, this approach was used in several fields including the

Fuzzy Logic and Neuro-Fuzzy Networks for Environmental Hazard Assessment 67

"Defuzzification" can be done using different methods, the most widely used one is the center of gravity, which calculates the center of gravity of the final fuzzy set and returns the

Fuzzification is a procedure through which the input variables are turned into fuzzy measures of their membership to given classes. Such a conversion from deterministic sizes to fuzzy sizes is performed through the membership functions pre-set for those classes. A membership function (Fig.2) is a function which associates a value (usually numerical) with the level of membership to the set. By convention, the real number which represents the level of membership [µ (x)] takes a 0 value when the element does not belong to the set, and

Fig. 1. Flow chart of the developed Fuzzy Inference System.

value of abscissa.

**1.1.1 Fuzzification** 

1 when it belongs to it completely.

Fig. 2. Membership function.

environment. In fact, it could be used for assessing environmental risk related to contamination of groundwater. The fuzzy approach is advantageous because it allows us a quick assessment of the risk, but is disadvantageous because of the increasing complexity in the definition of fuzzy rules along with the increasing of the number of parameters. In many situations, when the number of parameters are considered high in the analysis, application of these techniques is cumbersome and complex and could be used for neuro-fuzzy models. These models reduce the complexity because they use training data. The neuro-fuzzy model was supported by a sensitivity analysis in order to address the problem of subjectivity and uncertainty of model input data.

#### **1.1 Fuzzy logic**

Fuzzy logic is a binary logic, which is inspired by Buddhist philosophy, which considers the world as something continuous. The fuzzy logic theory derives from the Persian-American engineer, Lotfi Zadeh, who theorized it in 1965 in an article entitled "Information and Control". In traditional logic, Aristotelian principles of non-contradiction and the excluded middle are valid. The principle of non-contradiction states that if X is a generic set and x a generic element, then x may belong to the whole X or not. The fuzzy systems deal with data and their manipulation with greater flexibility than traditional systems. The binary logic (or classical) is only concerned with what is completely true and, as a result, with what is completely false. Fuzzy logic instead extends its interest even to what is not completely true, what is probable or uncertain. The fuzzy logic is based on a linguistic approach, in which words or phrases of natural language are used instead of numbers. This approach simplifies complex situations and concepts which may use the traditional logic. In particular, the fuzzy logic operates on mathematical entities that are fuzzy sets. Fuzzy sets obey rules, structures and axioms which are very similar to those of classical sets; the difference is that an object can simultaneously belong to several subsets, in contrast to the classical theory. In the fuzzy world, membership to a subset is associated to a degree of membership. The set of deduction rules to be applied to a given system to achieve results through the use of fuzzy logic is defined the fuzzy inference process. Main phases of the fuzzy approach (Fig. 1) are the following: definition of membership functions, fuzzification, inference and fuzzy output.

Definition of membership functions is the main step on which all the other subsequent operations are based. Such functions, representing the fuzzy sets, can take different shapes (trapezoidal, triangular, Gaussian, etc.) according to the situations, and by convention can take values included between 0 and 1.

The fuzzification is the process by which input variables are converted to fuzzy measures belonging to certain classes such as Very Low, Low, Medium, High, Very High. This operation normalizes all the data in the interval [0-1]. In this way, comparisons between different amounts, measured in different scales are also possible.

The inference is the phase in which rules of combination of fuzzy sets are applied and it is possible to deduce a result. The rules are linguistic expressions that are translated into a mathematical formalism with the exspression "if ... then" of the logic itself.

The output is a fuzzy membership value that can be used "pure" as a qualitative property or "defuzzificated", as a real number compatible with non-fuzzy approaches (Silvert, 2000).

"Defuzzification" can be done using different methods, the most widely used one is the center of gravity, which calculates the center of gravity of the final fuzzy set and returns the value of abscissa.

Fig. 1. Flow chart of the developed Fuzzy Inference System.

#### **1.1.1 Fuzzification**

66 Fuzzy Logic – Emerging Technologies and Applications

environment. In fact, it could be used for assessing environmental risk related to contamination of groundwater. The fuzzy approach is advantageous because it allows us a quick assessment of the risk, but is disadvantageous because of the increasing complexity in the definition of fuzzy rules along with the increasing of the number of parameters. In many situations, when the number of parameters are considered high in the analysis, application of these techniques is cumbersome and complex and could be used for neuro-fuzzy models. These models reduce the complexity because they use training data. The neuro-fuzzy model was supported by a sensitivity analysis in order to address the problem of subjectivity and

Fuzzy logic is a binary logic, which is inspired by Buddhist philosophy, which considers the world as something continuous. The fuzzy logic theory derives from the Persian-American engineer, Lotfi Zadeh, who theorized it in 1965 in an article entitled "Information and Control". In traditional logic, Aristotelian principles of non-contradiction and the excluded middle are valid. The principle of non-contradiction states that if X is a generic set and x a generic element, then x may belong to the whole X or not. The fuzzy systems deal with data and their manipulation with greater flexibility than traditional systems. The binary logic (or classical) is only concerned with what is completely true and, as a result, with what is completely false. Fuzzy logic instead extends its interest even to what is not completely true, what is probable or uncertain. The fuzzy logic is based on a linguistic approach, in which words or phrases of natural language are used instead of numbers. This approach simplifies complex situations and concepts which may use the traditional logic. In particular, the fuzzy logic operates on mathematical entities that are fuzzy sets. Fuzzy sets obey rules, structures and axioms which are very similar to those of classical sets; the difference is that an object can simultaneously belong to several subsets, in contrast to the classical theory. In the fuzzy world, membership to a subset is associated to a degree of membership. The set of deduction rules to be applied to a given system to achieve results through the use of fuzzy logic is defined the fuzzy inference process. Main phases of the fuzzy approach (Fig. 1) are the following: definition of membership functions, fuzzification, inference and fuzzy output. Definition of membership functions is the main step on which all the other subsequent operations are based. Such functions, representing the fuzzy sets, can take different shapes (trapezoidal, triangular, Gaussian, etc.) according to the situations, and by convention can

The fuzzification is the process by which input variables are converted to fuzzy measures belonging to certain classes such as Very Low, Low, Medium, High, Very High. This operation normalizes all the data in the interval [0-1]. In this way, comparisons between

The inference is the phase in which rules of combination of fuzzy sets are applied and it is possible to deduce a result. The rules are linguistic expressions that are translated into a

The output is a fuzzy membership value that can be used "pure" as a qualitative property or "defuzzificated", as a real number compatible with non-fuzzy approaches (Silvert, 2000).

different amounts, measured in different scales are also possible.

mathematical formalism with the exspression "if ... then" of the logic itself.

uncertainty of model input data.

take values included between 0 and 1.

**1.1 Fuzzy logic** 

Fuzzification is a procedure through which the input variables are turned into fuzzy measures of their membership to given classes. Such a conversion from deterministic sizes to fuzzy sizes is performed through the membership functions pre-set for those classes. A membership function (Fig.2) is a function which associates a value (usually numerical) with the level of membership to the set. By convention, the real number which represents the level of membership [µ (x)] takes a 0 value when the element does not belong to the set, and 1 when it belongs to it completely.

Fig. 2. Membership function.

Fuzzy Logic and Neuro-Fuzzy Networks for Environmental Hazard Assessment 69

<sup>2</sup>

1 *<sup>b</sup> f xabc*

Despite their simplicity, such functions cannot be used to represent asymmetry, which is

In order to face a possible asymmetry, we can use another type of function, such as the sigmoid function (Fig. 8), which may have left or right asymmetry and a horizontal

In addition to this function, we have further asymmetric functions, the Dsigm and Psigm membership functions represented in Fig. 9 and10 and described by Eq. (6), depending on

<sup>1</sup> *ax c f xac e* 

<sup>1</sup> *ax c f xac e* 

; ,

; ,

1

1

;,,

Fig. 5. Gauss membership function.

Fig. 6. Gauss2 membership function.

important in some applications.

four parameters a1, c1, a2 and c2.

Fig. 7. Generalized bell (Gbell) membership function.

asymptote. This function is ruled by parameters a and c (Eq. (5))

1

*x c a*

(4)

(5)

(6)

Membership functions can be of several types: the simplest are made up of straight lines, while the most used are the triangular (Fig. 3) and trapezoidal (Fig. 4) functions; the former are characterized by a triangular trend while the latter by a trapezoidal one. The advantage of these functions is in their simplicity. The triangular membership function depends on three scalar parameters a, b and c and is given by the following expression:

$$f(x;a,b,c) = \max\left(\min\left(\frac{x-a}{b-a}, \frac{c-x}{c-b}\right) 0\right) \tag{1}$$

while the trapezoidal one depends on four scalar parameters (a, b, c and d), as shown in the following formula:

$$f(x;a,b,c,d) = \max\left(\min\left(\frac{x-a}{b-a}, 1, \frac{d-x}{d-c}\right)0\right) \tag{2}$$

$$\sum\_{a=1}^{n} \left(\frac{x-a}{b-a}, \frac{x-a}{b-a}\right) \tag{3}$$

Fig. 3. Triangular membership function.

Fig. 4. Trapezoidal membership function.

There are other more complex functions, i.e. the Gauss function made up of a simple Gaussian curve (Fig. 5) which depends on parameters r and c (Eq. (3)); and the Gauss2 function (Fig. 6) given by the fusion of two different Gaussian functions and depending on four parameters: r1 and c1, which define the shape of the function in the left part, and r2 e c2, which define the shape of the function in the right part. Moreover, between these types of functions, there is the bell membership function (Gbell) (Fig. 7) which is a hybrid of the Gaussian function; it is mainly used to manage non-fuzzy sets and depends on three parameters: a, b and c (Eq. (4))

$$f\left(\mathbf{x}; \sigma, \mathbf{c}\right) = e^{\frac{-\left(\mathbf{x} - \mathbf{c}\right)^2}{2\sigma^2}}\tag{3}$$

Fig. 5. Gauss membership function.

68 Fuzzy Logic – Emerging Technologies and Applications

Membership functions can be of several types: the simplest are made up of straight lines, while the most used are the triangular (Fig. 3) and trapezoidal (Fig. 4) functions; the former are characterized by a triangular trend while the latter by a trapezoidal one. The advantage of these functions is in their simplicity. The triangular membership function depends on

while the trapezoidal one depends on four scalar parameters (a, b, c and d), as shown in the

There are other more complex functions, i.e. the Gauss function made up of a simple Gaussian curve (Fig. 5) which depends on parameters r and c (Eq. (3)); and the Gauss2 function (Fig. 6) given by the fusion of two different Gaussian functions and depending on four parameters: r1 and c1, which define the shape of the function in the left part, and r2 e c2, which define the shape of the function in the right part. Moreover, between these types of functions, there is the bell membership function (Gbell) (Fig. 7) which is a hybrid of the Gaussian function; it is mainly used to manage non-fuzzy sets and depends on three

*fx c e* 

<sup>2</sup> <sup>2</sup> ; ,

 2

(3)

*x c*

0,,1,minmax,,,; *cd*

 

 

0,,minmax,,; *bc*

 

*ab*

*ab*

   

> 

 

*xd*

*ax dcbaxf* (2)

 

*xc*

*ax cbaxf* (1)

three scalar parameters a, b and c and is given by the following expression:

following formula:

Fig. 3. Triangular membership function.

Fig. 4. Trapezoidal membership function.

parameters: a, b and c (Eq. (4))

Fig. 6. Gauss2 membership function.

Fig. 7. Generalized bell (Gbell) membership function.

Despite their simplicity, such functions cannot be used to represent asymmetry, which is important in some applications.

In order to face a possible asymmetry, we can use another type of function, such as the sigmoid function (Fig. 8), which may have left or right asymmetry and a horizontal asymptote. This function is ruled by parameters a and c (Eq. (5))

$$f\left(\mathbf{x}; a, c\right) = \frac{1}{1 + e^{-a\left(\mathbf{x} - c\right)}}\tag{5}$$

In addition to this function, we have further asymmetric functions, the Dsigm and Psigm membership functions represented in Fig. 9 and10 and described by Eq. (6), depending on four parameters a1, c1, a2 and c2.

$$f\left(\mathbf{x}; a, c\right) = \frac{1}{1 + c^{-a\left(\mathbf{x} - c\right)}}\tag{6}$$

Fuzzy Logic and Neuro-Fuzzy Networks for Environmental Hazard Assessment 71

After the definition of the fuzzy data which comes from the fuzzification process, it is necessary to insert in the decisional engine the rules which supply the fuzzy output. The rules are usually made up of an if–then–else structure, which in its turn is made up of an antecedent which defines the conditions, and a consequent which defines the action. For each input variable of the model, in the antecedent we have a clause of the type (x is L) where L is a linguistic label revealing a fuzzy set. In this way, the antecedent supplies a characterization of the condition of the system we want to model, namely its description in quantitative terms. Usually the antecedent includes a conjunction of clauses, one for each observed variable, while the condition of the consequent determines the condition of

In conclusion, a fuzzy system can be considered as a non-linear function which transforms a certain number of input variables into output ones through a set of fuzzy rules. In the application of rules, some of them often lead to the same consequence with different levels of strength: in these cases the common custom is choosing the highest value. Following this phase, which is defined fuzzy inference, it is necessary to turn the data coming from the evaluation of rules into real numerical data: this process is the opposite of input

Defuzzification consists in drawing the output deterministic value from the fuzzy model. A careful analysis of the problem is at the basis of a correct defuzzification: it can be linguistic, when the output is a predicate to which a level of membership is associated, or numerical, of ''crisp" type (non-fuzzy) (used in fuzzy control). Many criteria of defuzzification exist: often in engineering the choice depends on computational simplicity. The most used defuzzification

fuzzification, in fact it is called either output fuzzification or defuzzification.

Fig. 12. Pi membership function.

Fig. 13. S membership function.

**1.1.2 Fuzzy inference** 

**1.1.3 Defuzzification** 

methods are the following:

outputs.

Fig. 8. Sigmoidale (Sig) membership function.

Fig. 9. Dsig membership function.

Fig. 10. Psig membership function.

Three more membership functions correlated with them are functions Z (Eq. (7)), S and Pi. The first one is an asymmetric function open to the left, the second is open to the right, while the third one is asymmetric but closed at both ends (Fig. 11-13).

Fig. 11. Z membership function.

Fig. 12. Pi membership function.

70 Fuzzy Logic – Emerging Technologies and Applications

2

12 , <sup>2</sup>

*bx ab x b*

Three more membership functions correlated with them are functions Z (Eq. (7)), S and Pi. The first one is an asymmetric function open to the left, the second is open to the right,

while the third one is asymmetric but closed at both ends (Fig. 11-13).

*xa ab a x b a*

(7)

2 , <sup>2</sup>

*b a x b*

*x a*

1,

0,

Fig. 8. Sigmoidale (Sig) membership function.

Fig. 9. Dsig membership function.

Fig. 10. Psig membership function.

Fig. 11. Z membership function.

Fig. 13. S membership function.

#### **1.1.2 Fuzzy inference**

After the definition of the fuzzy data which comes from the fuzzification process, it is necessary to insert in the decisional engine the rules which supply the fuzzy output. The rules are usually made up of an if–then–else structure, which in its turn is made up of an antecedent which defines the conditions, and a consequent which defines the action. For each input variable of the model, in the antecedent we have a clause of the type (x is L) where L is a linguistic label revealing a fuzzy set. In this way, the antecedent supplies a characterization of the condition of the system we want to model, namely its description in quantitative terms. Usually the antecedent includes a conjunction of clauses, one for each observed variable, while the condition of the consequent determines the condition of outputs.

In conclusion, a fuzzy system can be considered as a non-linear function which transforms a certain number of input variables into output ones through a set of fuzzy rules. In the application of rules, some of them often lead to the same consequence with different levels of strength: in these cases the common custom is choosing the highest value. Following this phase, which is defined fuzzy inference, it is necessary to turn the data coming from the evaluation of rules into real numerical data: this process is the opposite of input fuzzification, in fact it is called either output fuzzification or defuzzification.

#### **1.1.3 Defuzzification**

Defuzzification consists in drawing the output deterministic value from the fuzzy model. A careful analysis of the problem is at the basis of a correct defuzzification: it can be linguistic, when the output is a predicate to which a level of membership is associated, or numerical, of ''crisp" type (non-fuzzy) (used in fuzzy control). Many criteria of defuzzification exist: often in engineering the choice depends on computational simplicity. The most used defuzzification methods are the following:

Fuzzy Logic and Neuro-Fuzzy Networks for Environmental Hazard Assessment 73

( ) *out*

*<sup>i</sup> out*

*y*

*y*

Whereas, the formula for discrete function is:

not consider the distribution of membership function.

other functions can be used, such as Dsigm, Psigm and Pi.

**2.1 Architecture of a neuro-fuzzy network** 

output.

**2. Fuzzy neural network** 

( )

*y dy*

( )

*y y*

 

( ) *i i*

*y*

*i*

(10)

(11)

*y y dy*

*i*

In *Largest of maximum,* the precise value of the variable output is one of which the fuzzy subset has the maximum truth value. The main disadvantage of this method is that it does

However, the *smallest of maximum method* obtained the minimum value in fuzzy set as

The fuzzy neural network essentially fills the gaps in the fuzzy systems as well as other neurals. The fuzzy inference requires heuristics and does not acquire knowledge from inputoutput relationships as do neural networks. The advantage of a fuzzy neural network compared to a neural structure is that it can be represented by "linguistic rules". The nodes that form a neuro-fuzzy network have weights which do not commonly occur in a system based on a neural network. The network training is done using back-propagation algorithms. The Anfis models (Zimmermann 1991) acquire knowledge from data using algorithms typical of neural networks. This is represented using fuzzy rules. Substantially, neural networks are structured on different levels, starting from the input and output related systems which generate fuzzy rules that guide the process of construction output. As in fuzzy logic, the end result is linked to the fuzzy rules and membership functions. The membership functions can be of various types. The simplest consists of straight lines, while the most used functions are triangular and trapezoidal. There are more complex functions such as the Gauss function which consists of a simple Gaussian curve and function Gauss2 formed by the merger of two different Gaussian functions. In addition, among the functions of this kind, there is a bell membership function (Gbell) which is a hybrid of Gaussian function, and is used primarily to manage non-fuzzy sets. In order to meet any asymmetry,

The scientific literature has various applications of fuzzy neural network from the classical management of Humanoid Robots that will replace humans in dangerous jobs in the medical field or in the field of services (Dusko Katic et al., 2003). The fuzzy neural network was also used in the study of time series of solar activity (Abdel-Fattah Attia et al., 2005), in the assessment of noise in the workplace (Zaheeruddin Garima, 2006) and many others.

The proposed forecasting model for assessing the environmental risk of contamination of aquifers is based on an Adaptive Neural Network Fuzzy Inference System (ANFIS)


Among the methods found in literature, the most common are the centroid and maximum methods.

In the middle of the maximum method, output is obtained as the arithmetic mean of the values of "y" where fuzzy set height is maximum.

B' is the fuzzy set inferred by rules and

$$\text{Mogt}(B') = \left\{ y \, \middle| \, \mu\_{\mathbb{B}^\circ}(y) = \sup\_{y \in B^\circ} \mu\_{\mathbb{B}^\circ}(y) \right\} \tag{8}$$

is the set value of "y" for which height "µB'(y)" is maximum.

Therefore, it has

$$\mathcal{Y}\_{out} = \frac{\int\_{\text{bigt}(\mathcal{B'})} y dy}{\int\_{\text{bigt}(\mathcal{B'})} dy} \tag{9}$$

whose geometric significance is shown in Figure 14:

Fig. 14. Geometric significance of the Middle of maximum defuzzification method.

The output of the *Centroid method* is obtained as the abscissa of the center of gravity inferred from the rules in the space of fuzzy sets of algorithm output. The formula in the case of continuous function is:

$$y\_{out} = \frac{\int y \mu(y) dy}{\int \mu(y) dy} \tag{10}$$

Whereas, the formula for discrete function is:

$$y\_{out} = \frac{\sum\_{i} y\_i \mu(y\_i)}{\sum\_{i} \mu(y\_i)} \tag{11}$$

In *Largest of maximum,* the precise value of the variable output is one of which the fuzzy subset has the maximum truth value. The main disadvantage of this method is that it does not consider the distribution of membership function.

However, the *smallest of maximum method* obtained the minimum value in fuzzy set as output.

#### **2. Fuzzy neural network**

72 Fuzzy Logic – Emerging Technologies and Applications

Centroid method: the chosen numerical value for the output is calculated as the centre

Bisector method: the output is the abscissa of the bisector of the area subtended to the

Middle of maximum method: the output value is determined as the average of

Largest of maximum method: the output numerical value is calculated as the maximum

Smallest of maximum method: the output value is represented by the output minimum

Among the methods found in literature, the most common are the centroid and maximum

In the middle of the maximum method, output is obtained as the arithmetic mean of the

( ') ( ) ( ) *B B*

( ')

*hgt B*

*<sup>y</sup> dy*

*out*

Fig. 14. Geometric significance of the Middle of maximum defuzzification method.

The output of the *Centroid method* is obtained as the abscissa of the center of gravity inferred from the rules in the space of fuzzy sets of algorithm output. The formula in the case of

( ')

*hgt B*

*hgt B y y Sup y* 

' ' '

*ydy*

*y B*

 

(8)

(9)

of mass of the fuzzy set.

maximum values (Mom: middle of maximum).

of the maximum (Lom: Largest of maximum).

value (Som: Smallest of maximum).

B' is the fuzzy set inferred by rules and

values of "y" where fuzzy set height is maximum.

is the set value of "y" for which height "µB'(y)" is maximum.

whose geometric significance is shown in Figure 14:

fuzzy data set.

methods.

Therefore, it has

continuous function is:

The fuzzy neural network essentially fills the gaps in the fuzzy systems as well as other neurals. The fuzzy inference requires heuristics and does not acquire knowledge from inputoutput relationships as do neural networks. The advantage of a fuzzy neural network compared to a neural structure is that it can be represented by "linguistic rules". The nodes that form a neuro-fuzzy network have weights which do not commonly occur in a system based on a neural network. The network training is done using back-propagation algorithms. The Anfis models (Zimmermann 1991) acquire knowledge from data using algorithms typical of neural networks. This is represented using fuzzy rules. Substantially, neural networks are structured on different levels, starting from the input and output related systems which generate fuzzy rules that guide the process of construction output. As in fuzzy logic, the end result is linked to the fuzzy rules and membership functions. The membership functions can be of various types. The simplest consists of straight lines, while the most used functions are triangular and trapezoidal. There are more complex functions such as the Gauss function which consists of a simple Gaussian curve and function Gauss2 formed by the merger of two different Gaussian functions. In addition, among the functions of this kind, there is a bell membership function (Gbell) which is a hybrid of Gaussian function, and is used primarily to manage non-fuzzy sets. In order to meet any asymmetry, other functions can be used, such as Dsigm, Psigm and Pi.

The scientific literature has various applications of fuzzy neural network from the classical management of Humanoid Robots that will replace humans in dangerous jobs in the medical field or in the field of services (Dusko Katic et al., 2003). The fuzzy neural network was also used in the study of time series of solar activity (Abdel-Fattah Attia et al., 2005), in the assessment of noise in the workplace (Zaheeruddin Garima, 2006) and many others.

#### **2.1 Architecture of a neuro-fuzzy network**

The proposed forecasting model for assessing the environmental risk of contamination of aquifers is based on an Adaptive Neural Network Fuzzy Inference System (ANFIS)

Fuzzy Logic and Neuro-Fuzzy Networks for Environmental Hazard Assessment 75

Groundwater intrinsic vulnerability has been assessed by a method of zoning for homogeneous areas: the GNDCI-CNR method (M. Civita, 1990). However, landfills hazard has been determined through the use of fuzzy logic and neuro-fuzzy parameters (input data) by considering morphological, hydrological and environmental parameters for each site, such as: water table depth, leachate production, volume and type of waste, landfill coverage, landfill activity and proximity to river. Some of these were obtained using GIS

**LANDFILL HAZARD GROUNDWATER** 

**GROUNDWATER POLLUTION RISK**

For the simple management algorithm, the parameters previously indicated were used to define three different fuzzy inferences, as shown in the conceptual scheme in Figure 17. The results obtained through the first two fuzzy inferences, defined as *site vulnerability* and *landfill potentiality* respectively, were then aggregated to the crisp parameter called *landfill*

As shown in Figure 17, *site vulnerability*, defined through acclivity, depth to water table and watercourse proximity, allowed us to obtain the site's predisposition to suffer from contamination, namely the site's propensity to be contaminated because of a possible leachate seepage. The increase in vulnerability is favoured by low slopes, proximity to surface watercourses (meant as index, so the higher the index the higher the site vulnerability) and reduced depth of the water table. Thus, the values of the three parameters are low when the trend to undergo contamination is high. On the contrary, the *landfill potential* evaluates the potential of a landfill to release contaminants by virtue of the waste volume and the leachate production. Therefore, with the increase of these two factors such potential will increase. The procedure to determine the *landfill hazard index* combines the results obtained by the two previous fuzzy diagrams with the addition of the *landfill conditions*. The array of required training algorithm has been constructed, considering that the increase in values of the three parameters in the subset result in an increase in the hazard of landfills. The end result of the neuro-fuzzy process has been achieved through the training data which provided a numerical value between 0 and 1 representing the hazard index. In addition to training data that facilitates the definition of fuzzy rules, it is necessary to determine for each of the three fuzzy inferences the following: the type of membership function and the classes (very high, high, medium, low, very low). In conclusion, the results relating to site vulnerability, the

**FUZZY LOGIC/NEURO-FUZZY SYSTEM** 

Fig. 16. Fuzzy and neuro-fuzzy models for the groundwater pollution risk.

*conditions*, by obtaining the hazard index of each landfill.

landfill potential and the landfill hazard have been obtained.

**SENSITIVITY ANALYSIS**

**VULNERABILITY**

applications.

(Zimmermann 1991; Jang. 1993). ANFIS algorithm allowed us to calibrate membership functions of the fuzzy inference training the Artificial Neural Network. In order to perform the training, the definition of a matrix of input parameters, a single output value and the number of times (numbers interpolating the training matrix) was necessary.

However, ANFIS models acquire knowledge from data using the typical neural networks algorithms but represent it using fuzzy rules.

TThese kind of neural networks are basically structured on five different levels which autonomously generate systems of fuzzy rules that guide the process of construction of the outputs, starting from related inputs and outputs.

Each node of the first level integrates the membership function associated with the represented fuzzy term. Variables Xi are the linguistic variables that are associated with terms placed in the nodes (A11 = Low, A21 = High etc.).

Fig. 15. Architecture of a neuro-fuzzy network.

Nodes of the second level incorporate the antecedents of fuzzy rules. Within these nodes, only an AND logical operation between the active inputs is performed.

In the third level, each node calculates the degree of fulfillment of each rule and returns a weighted term which enters as input in the corresponding node of the next level.

The nodes of this layer incorporate the resulting rules instead. Each node accepts the corresponding weight that comes from the previous level in input, in addition to all the input variables to the first level.

The fifth and last node simply performs the sum of all inputs and returns the final output of the system.

#### **3 Case study**

#### **3.1 Fuzzy and neuro-fuzzy models for groundwater pollution risk assessment**

This study proposes two methods for environmental risk assessment: fuzzy logic and fuzzyneural networks. Fuzzy and neuro-fuzzy models have been used to assess environmental risk in landfills, by using groundwater intrinsic vulnerability of landfill hazard (Fig. 17).

(Zimmermann 1991; Jang. 1993). ANFIS algorithm allowed us to calibrate membership functions of the fuzzy inference training the Artificial Neural Network. In order to perform the training, the definition of a matrix of input parameters, a single output value and the

However, ANFIS models acquire knowledge from data using the typical neural networks

TThese kind of neural networks are basically structured on five different levels which autonomously generate systems of fuzzy rules that guide the process of construction of the

Each node of the first level integrates the membership function associated with the represented fuzzy term. Variables Xi are the linguistic variables that are associated with

Nodes of the second level incorporate the antecedents of fuzzy rules. Within these nodes,

In the third level, each node calculates the degree of fulfillment of each rule and returns a

The nodes of this layer incorporate the resulting rules instead. Each node accepts the corresponding weight that comes from the previous level in input, in addition to all the

The fifth and last node simply performs the sum of all inputs and returns the final output of

This study proposes two methods for environmental risk assessment: fuzzy logic and fuzzyneural networks. Fuzzy and neuro-fuzzy models have been used to assess environmental risk in landfills, by using groundwater intrinsic vulnerability of landfill hazard (Fig. 17).

only an AND logical operation between the active inputs is performed.

weighted term which enters as input in the corresponding node of the next level.

**3.1 Fuzzy and neuro-fuzzy models for groundwater pollution risk assessment** 

number of times (numbers interpolating the training matrix) was necessary.

algorithms but represent it using fuzzy rules.

outputs, starting from related inputs and outputs.

Fig. 15. Architecture of a neuro-fuzzy network.

input variables to the first level.

the system.

**3 Case study** 

terms placed in the nodes (A11 = Low, A21 = High etc.).

Groundwater intrinsic vulnerability has been assessed by a method of zoning for homogeneous areas: the GNDCI-CNR method (M. Civita, 1990). However, landfills hazard has been determined through the use of fuzzy logic and neuro-fuzzy parameters (input data) by considering morphological, hydrological and environmental parameters for each site, such as: water table depth, leachate production, volume and type of waste, landfill coverage, landfill activity and proximity to river. Some of these were obtained using GIS applications.

Fig. 16. Fuzzy and neuro-fuzzy models for the groundwater pollution risk.

For the simple management algorithm, the parameters previously indicated were used to define three different fuzzy inferences, as shown in the conceptual scheme in Figure 17. The results obtained through the first two fuzzy inferences, defined as *site vulnerability* and *landfill potentiality* respectively, were then aggregated to the crisp parameter called *landfill conditions*, by obtaining the hazard index of each landfill.

As shown in Figure 17, *site vulnerability*, defined through acclivity, depth to water table and watercourse proximity, allowed us to obtain the site's predisposition to suffer from contamination, namely the site's propensity to be contaminated because of a possible leachate seepage. The increase in vulnerability is favoured by low slopes, proximity to surface watercourses (meant as index, so the higher the index the higher the site vulnerability) and reduced depth of the water table. Thus, the values of the three parameters are low when the trend to undergo contamination is high. On the contrary, the *landfill potential* evaluates the potential of a landfill to release contaminants by virtue of the waste volume and the leachate production. Therefore, with the increase of these two factors such potential will increase. The procedure to determine the *landfill hazard index* combines the results obtained by the two previous fuzzy diagrams with the addition of the *landfill conditions*. The array of required training algorithm has been constructed, considering that the increase in values of the three parameters in the subset result in an increase in the hazard of landfills. The end result of the neuro-fuzzy process has been achieved through the training data which provided a numerical value between 0 and 1 representing the hazard index. In addition to training data that facilitates the definition of fuzzy rules, it is necessary to determine for each of the three fuzzy inferences the following: the type of membership function and the classes (very high, high, medium, low, very low). In conclusion, the results relating to site vulnerability, the landfill potential and the landfill hazard have been obtained.

Fuzzy Logic and Neuro-Fuzzy Networks for Environmental Hazard Assessment 77

Fig. 18. Location of the uncontrolled landfills in the Basilicata Region.

Frequency

% cumulated

**Groundwater pollution risk classes (Neuro-fuzzy model)**

Fig. 19. Cumulated frequency curve of groundwater pollution risk for neuro-fuzzy model.

**Frequency**

0% 10% 20% 30% 40% 50% 60% 70% 80% 90% 100%

Among the three output values for each landfill, our attention was mostly focused on the landfill hazard.

Fig. 17. Conceptual diagram of the implemented fuzzy model.

In addition, to address the risk of subjectivity and to overcome the problem of uncertainty, linked to input data and to the developed models, sensitivity analysis has been used, through which different fuzzy and neuro -fuzzy schemes have been compared. The various fuzzy schemes differ in the type of membership functions and defuzzification methods. Then, each fuzzy scheme is characterized by "if-then" fuzzy rules, membership functions and defuzzification method. The fuzzy rules have been defined considering that groundwater pollution risk rises with the increase of groundwater intrinsic vulnerability and landfill hazard.

However, the neuro-fuzzy schemes differ only in the type of membership functions, while the fuzzy rules are automatically generated by the algorithm using the assigned training matrix. The results obtained from the simulations of both models were compared with input data to identify the best fuzzy and neuro-fuzzy scheme.

The proposed algorithms have been applied to some uncontrolled landfills present in the Basilicata Region, detected through the 2002 census ("Corpo Forestale dello Stato [Forest Rangers]" and "Regional Reclamation Plan"), which identified 469 areas needing reclamation actions, environmental recovery and/or safety measures: 315 in the province of Potenza and 204 in the province of Matera. Among these areas, 290 are illegal landfills (Fig. 18): 122 in the province of Matera and 168 in the province of Potenza.

The comparison of each fuzzy and neuro-fuzzy scheme has been performed by applying statistical tests to the distributions of output data (environmental risk index). The results show that the best scheme for the fuzzy model is characterized by Gauss2 membership functions and Centroid defuzzification method, and the best scheme of neuro-fuzzy model is marked by Gauss membership function. The final results show the environmental risk index and have been recalculated for a classification of groundwater pollution risk in linguistic terms by using a cumulative frequency distribution curve (Fig. 19 and 20).

Among the three output values for each landfill, our attention was mostly focused on the

In addition, to address the risk of subjectivity and to overcome the problem of uncertainty, linked to input data and to the developed models, sensitivity analysis has been used, through which different fuzzy and neuro -fuzzy schemes have been compared. The various fuzzy schemes differ in the type of membership functions and defuzzification methods. Then, each fuzzy scheme is characterized by "if-then" fuzzy rules, membership functions and defuzzification method. The fuzzy rules have been defined considering that groundwater pollution risk rises with the increase of groundwater intrinsic vulnerability

However, the neuro-fuzzy schemes differ only in the type of membership functions, while the fuzzy rules are automatically generated by the algorithm using the assigned training matrix. The results obtained from the simulations of both models were compared with

The proposed algorithms have been applied to some uncontrolled landfills present in the Basilicata Region, detected through the 2002 census ("Corpo Forestale dello Stato [Forest Rangers]" and "Regional Reclamation Plan"), which identified 469 areas needing reclamation actions, environmental recovery and/or safety measures: 315 in the province of Potenza and 204 in the province of Matera. Among these areas, 290 are illegal landfills (Fig.

The comparison of each fuzzy and neuro-fuzzy scheme has been performed by applying statistical tests to the distributions of output data (environmental risk index). The results show that the best scheme for the fuzzy model is characterized by Gauss2 membership functions and Centroid defuzzification method, and the best scheme of neuro-fuzzy model is marked by Gauss membership function. The final results show the environmental risk index and have been recalculated for a classification of groundwater pollution risk in

linguistic terms by using a cumulative frequency distribution curve (Fig. 19 and 20).

Fig. 17. Conceptual diagram of the implemented fuzzy model.

input data to identify the best fuzzy and neuro-fuzzy scheme.

18): 122 in the province of Matera and 168 in the province of Potenza.

landfill hazard.

and landfill hazard.

Fig. 18. Location of the uncontrolled landfills in the Basilicata Region.

Fig. 19. Cumulated frequency curve of groundwater pollution risk for neuro-fuzzy model.

Fuzzy Logic and Neuro-Fuzzy Networks for Environmental Hazard Assessment 79

Fuzzy model Neuro-fuzzy model

Fig. 21. Distributions of aquifers in classes of risk for fuzzy and neuro-fuzzy models.

We have evaluated the risk indices obtained from the two models for a more appropriate comparison. The assessment of the risk index without the subdivision into classes has demonstrated that the performance of the two distributions is very similar (Fig. 22) as

0 20 40 60 80 100 120

Fig. 22. Variation of the environmental risk index for each site.

Neuro-fuzzy model Fuzzy model

0% 10% 20% 30% 40% 50% 60% 70% 80% 90% 100%

confirmed by the box-plots (Fig. 23).

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

#### **3.2 Comparison between environmental risk results obtained from the fuzzy and neuro-fuzzy models**

The two designed models applied to some aquifers in Basilicata region have provided different results. For this reason, we next performed a statistical comparison. Visual analysis of histograms representing the percentage of aquifers falling in different classes of risk (fuzzy and neuro-fuzzy models) shows that distributions give different classes of risk (Fig. 21).

**Groundwater pollution risk classes (Fuzzy model)**

Fig. 20. Cumulated frequency curve of groundwater pollution risk for fuzzy model.

**3.2 Comparison between environmental risk results obtained from the fuzzy and** 

Fuzzy model Neuro-fuzzy model

The two designed models applied to some aquifers in Basilicata region have provided different results. For this reason, we next performed a statistical comparison. Visual analysis of histograms representing the percentage of aquifers falling in different classes of risk (fuzzy and neuro-fuzzy models) shows that distributions give different classes of risk (Fig. 21).

0

**neuro-fuzzy models** 

0%

10%

20%

30%

40%

50%

60%

70%

5

10

15

20

**Frequency**

25

30

35

40

Frequency % cumulated 0% 10% 20% 30% 40% 50% 60% 70% 80% 90% 100%

Very\_low Low Medium High Very\_high

Fig. 21. Distributions of aquifers in classes of risk for fuzzy and neuro-fuzzy models.

We have evaluated the risk indices obtained from the two models for a more appropriate comparison. The assessment of the risk index without the subdivision into classes has demonstrated that the performance of the two distributions is very similar (Fig. 22) as confirmed by the box-plots (Fig. 23).

Fig. 22. Variation of the environmental risk index for each site.

Fuzzy Logic and Neuro-Fuzzy Networks for Environmental Hazard Assessment 81

The fuzzy and neuro-fuzzy approaches used for the realization of models of environmental risk assessment have been fast, effective and affordable methods and at the same time useful support for decisions. The neuro-fuzzy model is faster in the application because by using training data, it is able to generate the fuzzy rules, which are particularly complex and

In addition, integration of sensitivity analysis in the two models is a positive element because it is able to mitigate the problems of subjectivity and arbitrariness of the evaluation based on fuzzy approaches commonly found in literature, in particular with regards to the choice of membership functions. The case study proposed, in fact, shows that by varying the choice of the membership functions very different results if not contradictory can be

In conclusion, a model can be substituted with the exception of the neuro-fuzzy model that is rapidly applicable in case you have data available for training a neuro-fuzzy network.

The fuzzy method is advantageous because it allows a rapid and efficient risk assessment and is an inexpensive and expeditious planning tool for a program of remediation. However, it is disadvantageous due to the complexity in the definition of fuzzy rules especially when the number of parameters is high. In fact, in many situations when the number of parameters of the analysis is high, the application of these techniques is cumbersome and complex; in these cases, neuro-fuzzy models, that reduce the complexity of the models thanks to the training data, could be used. Using the adaptive methods of fuzzy inference neural networks, you can easily manage fuzzy rules of the analysis and reduce the

The use of this kind of analysis with respect to neural models does not provide very different results, as assessed and analyzed even by Vieira et al. in 2004, but only a different

Abdel-Fattah, Attia, Rabab, Abdel-Hamid, & Maha, Quassim (2005). Prediction of solar

Caniani, D., Lioi, D.S., Mancini, I.M., & Masi, S. (2011). Application of fuzzy logic and

Civita, M.; (1990) Legenda unicata per le Carte della vulnerabilità dei corpi idrici

Skarlatos, Dimitris, Karakasis, Kleomenis, & Trochidis, Athanassios, (2004)Railway wheel fault diagnosis using a fuzzy-logic method. *Applied Acoustics*, 65 (2004) 951–966. Duško, Katic, & Miomir, Vukobratovic (2003). Survey of Intelligent Control Techniques for Humanoid Robots. *Journal of Intelligent and Robotic Systems*, 37-117-141. Hitoshi, Iyatomi, & Masafumi, Hagiwara (2004). Adaptive fuzzy inference neural network.

sensitivity analysis for soil contamination hazard classification. *Waste Management*

sotterranei/ Unified legend for the groundwater pollution vulnerability Maps.

activity based on neuro-fuzzy modeling, *Solar Physics* 227: 177–191.

*Studi sulla Vulnerabilità degli Acquiferi*, 1 Pitagora, Bologna

increases along with the number of parameters assigned to the model.

artifices of fuzzy and neural models (Iyatomi et al., 2004).

training time influenced by the order of the model.

*Pattern Recognition* 37 2049-2057.

**4. Conclusion** 

obtained.

**5. References** 

31 583–594.

Fig. 23. Box-plots of the distributions of output data for fuzzy and neuro-fuzzy models.

Fig. 24. Scatter plot between the environmental risk index obtained from the fuzzy and neuro-fuzzy models.

In fact, even the scatter plot (Fig. 24) shows a good correlation as evaluated by the coefficient of determination R2,which is the square of the correlation coefficient R = 0.8832. Moreover, similarity between results of the two models can also be inferred from the comparison between variances and standard distributions and F test (Table 1).


Table 1. Statistical indices and test F results.

#### **4. Conclusion**

80 Fuzzy Logic – Emerging Technologies and Applications

Fuzzy model Neuro-fuzzy model

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

In fact, even the scatter plot (Fig. 24) shows a good correlation as evaluated by the coefficient of determination R2,which is the square of the correlation coefficient R = 0.8832. Moreover, similarity between results of the two models can also be inferred from the comparison

Environmental risk index

(Fuzzy model)

Fig. 24. Scatter plot between the environmental risk index obtained from the fuzzy and

between variances and standard distributions and F test (Table 1).

Standard deviation 0.136 0.133 Variance 0.018 0.018 R² = 0.780

Environmental risk index (Neuro-fuzzy model)

Fig. 23. Box-plots of the distributions of output data for fuzzy and neuro-fuzzy models.

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

neuro-fuzzy models.

F test 0.870

Table 1. Statistical indices and test F results.

The fuzzy and neuro-fuzzy approaches used for the realization of models of environmental risk assessment have been fast, effective and affordable methods and at the same time useful support for decisions. The neuro-fuzzy model is faster in the application because by using training data, it is able to generate the fuzzy rules, which are particularly complex and increases along with the number of parameters assigned to the model.

In addition, integration of sensitivity analysis in the two models is a positive element because it is able to mitigate the problems of subjectivity and arbitrariness of the evaluation based on fuzzy approaches commonly found in literature, in particular with regards to the choice of membership functions. The case study proposed, in fact, shows that by varying the choice of the membership functions very different results if not contradictory can be obtained.

In conclusion, a model can be substituted with the exception of the neuro-fuzzy model that is rapidly applicable in case you have data available for training a neuro-fuzzy network.

The fuzzy method is advantageous because it allows a rapid and efficient risk assessment and is an inexpensive and expeditious planning tool for a program of remediation. However, it is disadvantageous due to the complexity in the definition of fuzzy rules especially when the number of parameters is high. In fact, in many situations when the number of parameters of the analysis is high, the application of these techniques is cumbersome and complex; in these cases, neuro-fuzzy models, that reduce the complexity of the models thanks to the training data, could be used. Using the adaptive methods of fuzzy inference neural networks, you can easily manage fuzzy rules of the analysis and reduce the artifices of fuzzy and neural models (Iyatomi et al., 2004).

The use of this kind of analysis with respect to neural models does not provide very different results, as assessed and analyzed even by Vieira et al. in 2004, but only a different training time influenced by the order of the model.

#### **5. References**


**5** 

Yetis Sazi Murat

 *Turkey* 

 *Civil Engineering Department, Transportation Division, Denizli,* 

Number of Dead people (per 100 million veh-km)

**Fuzzy Clustering Approach** 

*Pamukkale University, Faculty of Engineering,* 

**for Accident Black Spot Centers Determination** 

Traffic accident rates of Turkey are higher than most of the European Union countries and other countries in the world (Table 1). Every year, almost more than 8000 people die by traffic accidents in Turkey. This figure is very high comparing to many countries at same size. There have been many projects conducted by national or international organizations for decreasing these rates. In order to develop sustainable prevention models, accidents

Traffic accident data can be analyzed in different ways, based on amount and types of data. The analysis is not complicated if the data are smooth and not dispersed. But it is not an easy task if the data are scattered. Although there is not a general definition for black spots, locations where at least more than one accident occured are treated as black spots. Based on this definition, the number of black spots can be increased and analysis of them is getting

should be analyzed in detail considering primary and secondary reasons.

100 million veh-km)

USA 58 0.3 England 60 1 Germany 351 1 Japan 111 1.4 France 27 1.9 Türkiye 108 7.5

Several methods can be used for determination of black spots and centers. It can be determined by eye using simple observations. But this simple approach can include subjective perceptions and also results obtained can not be sensitive and scientific. Besides to locations, other specifications of black spots should be taken into consideration for a scientific analysis. Developing countermeasures and classifying by characteristics for black spots that are intensified and covered whole area on the map is not an easy task. Although

Country Number of İnjured people (per

Table 1. Traffic Accident rates (Murat and Sekerler, 2009)

**1. Introduction** 

more difficult.


### **Fuzzy Clustering Approach for Accident Black Spot Centers Determination**

#### Yetis Sazi Murat

*Pamukkale University, Faculty of Engineering, Civil Engineering Department, Transportation Division, Denizli, Turkey* 

#### **1. Introduction**

82 Fuzzy Logic – Emerging Technologies and Applications

Mei-qin, LIU, Sen-lin, Zhang, & Gang-feng, YAN, (2008). A new neural network model for

Miha, Mraz, (2001) The design of intelligent control of a kitchen refrigerator. *Mathematics and* 

Saad, R., & Halgamuge, S. K., (2004). Stability of hierarchical fuzzy systems generated by

Silvert, William, (2000) Fuzzy indices of environmental conditions. *Ecological Modelling* 130,

Van der Wal, A.J., (1995), Application of fuzzy logic control in industry. *Fuzzy Sets and* 

Vieira, Josè, Fernando, Morgado Dias, & Alexandre, Mota (2004). Artificial neural networks

Zaheeruddi, Garima(2006). A neuro-fuzzy approach for prediction of human work

Zimmermann, H.-J. (1991). Fuzzy set theory and its applications, Dordrecht: Kluwer, second

study, *Engineering Applications of Artificial Intelligence*, 17 265–273.

efficiency in noisy environment. *Applied Soft Computing* 6 283-294.

Zadeh, L.A.; ( 1965) Information and control; *Fuzzy sets* 338-353 (1965).

and neuro-fuzzy systems for modelling and controlling real systems: a comparative

Saltelli, A., Chan, K., & Scott, E.M., (2000) Sensitivity analysis, Wiley & Sons

9(8):1015-1023.

111–119.

edition.

*Systems*, 74 33-41(1995).

*Computers in Simulation*, 56 259–267

Neuro-Fuzzy, *Soft Computing* 8 409–416.

the feedback stabilization of nonlinear systems, Liu et al. / J Zhejiang Univ Sci A

Traffic accident rates of Turkey are higher than most of the European Union countries and other countries in the world (Table 1). Every year, almost more than 8000 people die by traffic accidents in Turkey. This figure is very high comparing to many countries at same size. There have been many projects conducted by national or international organizations for decreasing these rates. In order to develop sustainable prevention models, accidents should be analyzed in detail considering primary and secondary reasons.

Traffic accident data can be analyzed in different ways, based on amount and types of data. The analysis is not complicated if the data are smooth and not dispersed. But it is not an easy task if the data are scattered. Although there is not a general definition for black spots, locations where at least more than one accident occured are treated as black spots. Based on this definition, the number of black spots can be increased and analysis of them is getting more difficult.


Table 1. Traffic Accident rates (Murat and Sekerler, 2009)

Several methods can be used for determination of black spots and centers. It can be determined by eye using simple observations. But this simple approach can include subjective perceptions and also results obtained can not be sensitive and scientific. Besides to locations, other specifications of black spots should be taken into consideration for a scientific analysis. Developing countermeasures and classifying by characteristics for black spots that are intensified and covered whole area on the map is not an easy task. Although

Fuzzy Clustering Approach for Accident Black Spot Centers Determination 85

collision risks of motor vehicles and bicycles is developed by Wang and Nihan (2004). They classified the accidents considering movements of traffic flows such as through, right turning, and left turning. A probability based method is used in the research. Three negative binomial regression models are improved in the study. The study showed that Negative Binomial regression approach can be used instead of Poisson regression approach. Abdel-Aty and Pange (2007) investigated crash data in two levels (i.e.collective and individual level). They focused real time estimation of crash likelihood and discussed advantages and disadvantages of the analysis in two levels. Saploğlu and Karaşahin (2006) examined traffic accidents of Isparta, Turkey using Geographical Information Systems. They determined black spots and found that there is an increase in number of black spots by the years. They also emphasized that most of the accidents are occurred in junctions. Another remarkable study has been accomplished in Singapore. Kamalasudhan et al. (2000) obtained accident density map using digital accident data. They searched black spots or hot spots using the accident density map. The types of accidents by the days, hours, pavement conditions and

Individual analysis of traffic accidents has been taken into consideration in most of the studies given in literature. Besides, analysis of density (i.e. densely recorded area) and determination of black spots are also very important for traffic safety researches. On the other hand, determination of black spots and their center is not an easy task and need to be made many trials. To handle this problem, cluster analysis approach is used in the research. The main objectives of this paper are determination of black spots' center by k-means and

In recent years, cluster analysis has been widely used in the engineering application such as civil engineering, target recognition, medical diagnosis etc. Cluster analysis is an unsupervised method for classifying data, i.e. to divide a given data into a set of classes or

K-means clustering approach is one of the popular methods used in industrial and scientific areas. Euclidian distance is used in k-means clustering algorithm. In this analysis, the desired number of clusters should be determined in the beginning. The following objective

1 1

*j i J xc* 

*k n*

<sup>2</sup> ( )

(1)

*<sup>i</sup> x* and the corresponding center ( *<sup>j</sup> c* ).

*j i j*

fuzzy clustering approaches and analysis of these points to reveal main reasons.

vehicle types are analyzed in the study.

**3. Cluster analysis approaches** 

**3.1 Conventional (K-Means) clustering** 

function is tried to be minimized in this approach.

*<sup>i</sup> <sup>j</sup> x c* is the distance between the data ( )*<sup>j</sup>*

The following steps are used in k-means clustering approach.

clusters.

where,

<sup>2</sup> ( )*<sup>j</sup>*

J is total distance.

some black spots can have common characteristics, they can be located far away from each other. On the other hand, characteristics of black spots that are closely located to each other can be different. Therefore definition and analysis of black spots include uncertainties and conventional approaches can not be used for this purpose. In this study, cluster analysis approach is used for determination of black spots center and definition of the centers. Two types of analysis as k-means and fuzzy c-means are used. The (hard) k-means clustering approach is used as conventional method. In k-means clustering, the boundaries of clusters are determined as crisp. Thus some black spots that belong to a cluster based on their characteristics can be defined in different cluster by k-means clustering approach. But it can be defined in both clusters. To remove this deficiency, fuzzy c-means clustering approach is used. Fuzzy c-means are used for representing uncertainties in belonging to clusters. Thus some black spots are treated as members of two centers with two membership (belonging) values. In addition to determination of black spots centers, associative factors about the black spots are analyzed and discussed in the research.

In this study, first the black spots are determined using the data provided from Local Police Department, after that, the centers where black spots are intensified are revealed. These centers and the black spots around are considered in detail, the reasons of common results and findings are searched.

#### **2. Literature review**

There have been numerous studies about traffic safety. In this study, only GIS based studies and some important researches that include cluster analysis are taken into account and summarized.

Cluster analysis has been used in modeling traffic accident data by many researchers. Wong et al.(2004) used cluster analysis to develop a qualitative assessment methodology. Yannis et al. (2007) proposed a multilevel negative binomial modeling approach for the regional effect of enforcement on road accidents at Greece using cluster analysis. They made geographical and mathematical cluster analysis and reported that alcohol enforcement is the most significant one among the various types of enforcement.

Abdel-Aty and Radwan (2000), used Negative Binomial Distribution for modeling traffic accident occurrence and involvement. The models indicated that young and older drivers experience more accidents than middle aged drivers in heavy traffic volume, and reduced shoulder and median widths. They also obtained that heavy traffic volume, speeding, narrow lane width, larger number of lanes, urban roadway sections, narrow shoulder width and reduced median width increase the likelihood for accident involvement. Ng et al. (2002) aimed at developing an algorithm to estimate the number of traffic accidents and assess the risk of traffic accidents in Hong Kong. They presented an algorithm that involves a combination of mapping technique (Geographical Information System (GIS) techniques) and statistical methods. The results showed that the algorithm improves accident risk estimation when comparing to the estimated risk based on only the historical accident records. Abdel-Aty (2003) analyzed driver injury severity using ordered probit modeling approach. The models consider showed the significance of driver's age, gender, and seat belt use, point of impact, speed, and vehicle type on the injury severity level. An estimation model for

some black spots can have common characteristics, they can be located far away from each other. On the other hand, characteristics of black spots that are closely located to each other can be different. Therefore definition and analysis of black spots include uncertainties and conventional approaches can not be used for this purpose. In this study, cluster analysis approach is used for determination of black spots center and definition of the centers. Two types of analysis as k-means and fuzzy c-means are used. The (hard) k-means clustering approach is used as conventional method. In k-means clustering, the boundaries of clusters are determined as crisp. Thus some black spots that belong to a cluster based on their characteristics can be defined in different cluster by k-means clustering approach. But it can be defined in both clusters. To remove this deficiency, fuzzy c-means clustering approach is used. Fuzzy c-means are used for representing uncertainties in belonging to clusters. Thus some black spots are treated as members of two centers with two membership (belonging) values. In addition to determination of black spots centers, associative factors about the

In this study, first the black spots are determined using the data provided from Local Police Department, after that, the centers where black spots are intensified are revealed. These centers and the black spots around are considered in detail, the reasons of common results

There have been numerous studies about traffic safety. In this study, only GIS based studies and some important researches that include cluster analysis are taken into account and

Cluster analysis has been used in modeling traffic accident data by many researchers. Wong et al.(2004) used cluster analysis to develop a qualitative assessment methodology. Yannis et al. (2007) proposed a multilevel negative binomial modeling approach for the regional effect of enforcement on road accidents at Greece using cluster analysis. They made geographical and mathematical cluster analysis and reported that alcohol enforcement is the most

Abdel-Aty and Radwan (2000), used Negative Binomial Distribution for modeling traffic accident occurrence and involvement. The models indicated that young and older drivers experience more accidents than middle aged drivers in heavy traffic volume, and reduced shoulder and median widths. They also obtained that heavy traffic volume, speeding, narrow lane width, larger number of lanes, urban roadway sections, narrow shoulder width and reduced median width increase the likelihood for accident involvement. Ng et al. (2002) aimed at developing an algorithm to estimate the number of traffic accidents and assess the risk of traffic accidents in Hong Kong. They presented an algorithm that involves a combination of mapping technique (Geographical Information System (GIS) techniques) and statistical methods. The results showed that the algorithm improves accident risk estimation when comparing to the estimated risk based on only the historical accident records. Abdel-Aty (2003) analyzed driver injury severity using ordered probit modeling approach. The models consider showed the significance of driver's age, gender, and seat belt use, point of impact, speed, and vehicle type on the injury severity level. An estimation model for

black spots are analyzed and discussed in the research.

significant one among the various types of enforcement.

and findings are searched.

**2. Literature review** 

summarized.

collision risks of motor vehicles and bicycles is developed by Wang and Nihan (2004). They classified the accidents considering movements of traffic flows such as through, right turning, and left turning. A probability based method is used in the research. Three negative binomial regression models are improved in the study. The study showed that Negative Binomial regression approach can be used instead of Poisson regression approach. Abdel-Aty and Pange (2007) investigated crash data in two levels (i.e.collective and individual level). They focused real time estimation of crash likelihood and discussed advantages and disadvantages of the analysis in two levels. Saploğlu and Karaşahin (2006) examined traffic accidents of Isparta, Turkey using Geographical Information Systems. They determined black spots and found that there is an increase in number of black spots by the years. They also emphasized that most of the accidents are occurred in junctions. Another remarkable study has been accomplished in Singapore. Kamalasudhan et al. (2000) obtained accident density map using digital accident data. They searched black spots or hot spots using the accident density map. The types of accidents by the days, hours, pavement conditions and vehicle types are analyzed in the study.

Individual analysis of traffic accidents has been taken into consideration in most of the studies given in literature. Besides, analysis of density (i.e. densely recorded area) and determination of black spots are also very important for traffic safety researches. On the other hand, determination of black spots and their center is not an easy task and need to be made many trials. To handle this problem, cluster analysis approach is used in the research. The main objectives of this paper are determination of black spots' center by k-means and fuzzy clustering approaches and analysis of these points to reveal main reasons.

#### **3. Cluster analysis approaches**

In recent years, cluster analysis has been widely used in the engineering application such as civil engineering, target recognition, medical diagnosis etc. Cluster analysis is an unsupervised method for classifying data, i.e. to divide a given data into a set of classes or clusters.

#### **3.1 Conventional (K-Means) clustering**

K-means clustering approach is one of the popular methods used in industrial and scientific areas. Euclidian distance is used in k-means clustering algorithm. In this analysis, the desired number of clusters should be determined in the beginning. The following objective function is tried to be minimized in this approach.

$$J = \sum\_{j=1}^{k} \sum\_{i=1}^{n} \left\| \mathbf{x}\_i^{(j)} - \mathbf{c}\_j \right\|^2 \tag{1}$$

where, <sup>2</sup> ( )*<sup>j</sup> <sup>i</sup> <sup>j</sup> x c* is the distance between the data ( )*<sup>j</sup> <sup>i</sup> x* and the corresponding center ( *<sup>j</sup> c* ).

J is total distance.

The following steps are used in k-means clustering approach.

Fuzzy Clustering Approach for Accident Black Spot Centers Determination 87

function of feature vector, *m*[1 ∞] is weight exponent for each fuzzy membership and it determines the fuzziness of the clusters and controls the extent of membership shared among the fuzzy clusters. *U*, which is given in equation (7), is the fuzzy partition matrix which contains the membership of each feature vector in each fuzzy cluster. It should be

(,)(,) (,) *<sup>T</sup>*

11 1 1

*uu u*

*i ik iN*

*uu u*

i. Initialize fuzzy partition matrix U or Fuzzy cluster centroid matrix V using a random

ii. If the FCM algorithm is initialized with fuzzy partition matrix, the initial memberships

*u for i c k N*

iii. If the FCM algorithm is initialized with fuzzy cluster centroid matrix containing the fuzzy cluster centroid, memberships belonging to cluster is determined using equation

> 1 1

 

<sup>1</sup> ( ) (,) 1 ,1 <sup>1</sup> ( ) (,)

*dxv u for <sup>i</sup> <sup>c</sup> <sup>k</sup> <sup>N</sup>*

The steps (iii) and (iv) are repeated until the change in the value of memberships between

The main problem in fuzzy clustering is that the number of clusters (*c*) must be specified beforehand. Selections of a different number of initial clusters result in different clustering

( ) ( )

*u*

*u x*

*N m ik k k <sup>i</sup> <sup>N</sup> <sup>m</sup> ik k*

1 ,1

(8)

(9)

(10)

.....

*k N*

.....

.....

*c ck cN cxN*

1

*U uu u*

The procedure of FCM based on iterative optimization (Bezdek, 1981) can be given as;

..

.

1

*ki ki iki d x v x v Ax v* (6)

(7)

noted that, sum of membership values for a cluster must be equal to 1.

2

belonging to cluster is adjusted using equation (8).

iv. *<sup>i</sup> v* fuzzy centroid is computed by equation (9),

2

2 1

two iterations is sufficiently small level.

*dxv*

1

*u*

*v*

1/( 1)

*m*

1/( 1)

v. The fuzzy membership ( *uik* ) is updated by equation (10),

*k i ik <sup>c</sup> <sup>m</sup> i k i*

*u*

*initial ik ik <sup>c</sup> initial ik i*

number generator.

(9).

**3.1 Validation** 


One of the main disadvantages of this approach is determination of number of clusters in the beginning. Another disadvantage is sensitivity of the algorithm to the outliers.

#### **3.2 Fuzzy C-Means clustering**

Fuzzy C-Means (FCM) clustering algorithm has been widely used and applied in different areas. The description of the original fuzzy clustering algorithm based on objective function dates back to 1973 (Bezdek, 1973; Dunn, 1974). This algorithm was conceived in 1973 by Dunn (1974) and further generalized by Bezdek (1973). Among the existing fuzzy clustering methods, the Fuzzy c-means (FCM) algorithm proposed by Bezdek (1981) is the simplest and is the most popular technique of clustering. It is an extension of the hard K-means algorithm to fuzzy framework. Grubesic (2006) explored the use of a generalized partitioning method known as fuzzy clustering for crime hot-spot detection.

FCM algorithm is extension of Hard K-means with advantage of fuzzy set theory and contrary to the K-means method the FCM is more flexible because it shows those objects that have some interface with more than one cluster in the partition. In traditional clustering algorithms such as Hard K-Means, an element belongs fully to a cluster or not (i.e. 0 or 1). On the other hand, in Fuzzy clustering, each element can belongs to several clusters with different membership degrees. The main goal of any clustering algorithm is to determine appropriate the partition matrix *U(X)* of a given data set *X* consisting of patterns ( *X xx x* 1 2 , ........ *<sup>N</sup>* ) and to find the appropriate number of clusters. The objective function and constraints can be defined as;

Objective function

$$f(X; \mathcal{U}, V) = \sum\_{i=1}^{c} \sum\_{k=1}^{N} (\mu\_{ik})^m d^2(x\_{k'} v\_i) \tag{2}$$

$$V = \left[v\_1, v\_2, \dots, v\_c\right], \ v\_i \in \mathbb{R}^n \tag{3}$$

Constraints

$$\sum\_{i=1}^{c} \mu\_{ik} = 1 \quad \forall \, k \in \{1, \dots, N\} \tag{4}$$

$$0 \prec \sum\_{i=1}^{c} \mu\_{ik} \prec N \quad \forall \ i \in \{1, \ldots, c\} \tag{5}$$

Where, *c* is the number of cluster, *<sup>i</sup> v* is the centroid, *d* is the Euclidian distance between rescaled feature vector and centroid of cluster, *uik* [0,1] denotes the degree of membership

One of the main disadvantages of this approach is determination of number of clusters in

Fuzzy C-Means (FCM) clustering algorithm has been widely used and applied in different areas. The description of the original fuzzy clustering algorithm based on objective function dates back to 1973 (Bezdek, 1973; Dunn, 1974). This algorithm was conceived in 1973 by Dunn (1974) and further generalized by Bezdek (1973). Among the existing fuzzy clustering methods, the Fuzzy c-means (FCM) algorithm proposed by Bezdek (1981) is the simplest and is the most popular technique of clustering. It is an extension of the hard K-means algorithm to fuzzy framework. Grubesic (2006) explored the use of a generalized

FCM algorithm is extension of Hard K-means with advantage of fuzzy set theory and contrary to the K-means method the FCM is more flexible because it shows those objects that have some interface with more than one cluster in the partition. In traditional clustering algorithms such as Hard K-Means, an element belongs fully to a cluster or not (i.e. 0 or 1). On the other hand, in Fuzzy clustering, each element can belongs to several clusters with different membership degrees. The main goal of any clustering algorithm is to determine appropriate the partition matrix *U(X)* of a given data set *X* consisting of patterns ( *X xx x* 1 2 , ........ *<sup>N</sup>* ) and to find the appropriate number of clusters. The objective function

> 1 1 (;,) ( ) ( ,) *c N <sup>m</sup>*

1 1,.......

*u Ni c*

*ukN*

0 1,.......

Where, *c* is the number of cluster, *<sup>i</sup> v* is the centroid, *d* is the Euclidian distance between rescaled feature vector and centroid of cluster, *uik* [0,1] denotes the degree of membership

*i k*

*JXUV*

1

1

*c ik i*

*c ik i*

2

*dxv*

*ik k i*

(2)

1 2 , ,..... , *<sup>n</sup> V vv v v R c i* (3)

(4)

(5)

the beginning. Another disadvantage is sensitivity of the algorithm to the outliers.

partitioning method known as fuzzy clustering for crime hot-spot detection.

Select the number of cluster centers (k)

**3.2 Fuzzy C-Means clustering** 

and constraints can be defined as;

Objective function

Constraints

Assign each object to the nearest cluster center group

Repeat 2nd and 3rd steps till the cluster centers are fixed

After assigning all objects, recalculate locations of cluster center

function of feature vector, *m*[1 ∞] is weight exponent for each fuzzy membership and it determines the fuzziness of the clusters and controls the extent of membership shared among the fuzzy clusters. *U*, which is given in equation (7), is the fuzzy partition matrix which contains the membership of each feature vector in each fuzzy cluster. It should be noted that, sum of membership values for a cluster must be equal to 1.

$$d^2(\mathbf{x}\_k, \upsilon\_i) = (\mathbf{x}\_k, \upsilon\_i)^T A\_i(\mathbf{x}\_k, \upsilon\_i) \tag{6}$$

$$\mathbf{U} = \begin{bmatrix} u\_{11} & u\_{1k} & \dots & u\_{1N} \\ \vdots & & \\ u\_{i1} & u\_{ik} & \dots & u\_{iN} \\ \vdots & & \\ u\_{c1} & u\_{ck} & \dots & u\_{cN} \end{bmatrix}\_{\text{ccN}} \tag{7}$$

The procedure of FCM based on iterative optimization (Bezdek, 1981) can be given as;


$$\mu\_{ik} = \frac{\mathbf{u}\_{ik}^{initial}}{\sum\_{i=1}^{c} \mathbf{u}\_{ik}^{initial}} \qquad \text{for } 1 \le i \le c, \ 1 \le k \le N \tag{8}$$


$$\upsilon\_i = \frac{\sum\_{k=1}^{N} (\mu\_{ik})^m x\_k}{\sum\_{k=1}^{N} (\mu\_{ik})^m} \tag{9}$$

v. The fuzzy membership ( *uik* ) is updated by equation (10),

$$u\_{ik} = \frac{(\frac{1}{d^2(\mathbf{x}\_{k'}, \upsilon\_i)})^{1/(m-1)}}{\sum\_{i=1}^c (\frac{1}{d^2(\mathbf{x}\_{k'}, \upsilon\_i)})^{1/(m-1)}} \qquad \text{for } 1 \le i \le c, \ 1 \le k \le N \tag{10}$$

The steps (iii) and (iv) are repeated until the change in the value of memberships between two iterations is sufficiently small level.

#### **3.1 Validation**

The main problem in fuzzy clustering is that the number of clusters (*c*) must be specified beforehand. Selections of a different number of initial clusters result in different clustering

Fuzzy Clustering Approach for Accident Black Spot Centers Determination 89

min ( , ) ( ) min min , max max ( , )

In this study, Denizli that is a medium sized city (current population is about 700000) of Turkey is considered. Traffic accident records for the years of 2004, 2005 and 2006 are used in analyzing accidents. The accident reports are provided by Local Police Department. All of the data and documents are taken from an ongoing research project. Following information

*dxy DI c i k*

Road and environmental conditions (signal, pavement, policeman, obstacle etc.)

Crossings (school crossing, pedestrian crossing, railroad crossing)

are analyzed using k-means and fuzzy clustering approaches.

 Information about vehicles (type, model, damage condition, speed etc) Information about drivers (age, sex, alcohol, usage of safety belt etc )

Information about passengers and pedestrians (age, sex, alcohol, usage of safety belt etc )

All of these data given above are recorded using first MS Excel. Then, coordinates of each accident point are determined using street definition system in MAPINFO software. The data from Excel data base including coordinates of the accident points are transferred to MAPINFO data base. This data base is constituted for accident analysis by inquiring different attribution of each accident. Thus, traffic accident can be evaluated from different points of view and the relations about reasons and results of accidents can be revealed by

The data related to coordinates of accidents (locations) are used in cluster analysis. The Figure 1 shows sample processed data on Denizli city GIS map (Murat et al, 2008). The data

*ic kc*

**4. Study area and available data** 

Location of accident (coordinates)

Accident type for occurrence

 Problems based on roadway Presence of warning sign Vertical route conditions Horizontal route conditions Intersection conditions

Vehicle insurance conditions

these analysis.

Road direction type (one or two way)

Accident type for participating vehicle number

Pavement surface conditions (dry, wet, icy etc.)

Other factors (narrow road, bridge, tunnel)

are collected from the reports:

Type of accident

Weather condition

Type of pavement

 Date Time  , ,

*dxy*

(16)

*<sup>i</sup> x C y Ck*

*k C xy C*

partitions. Therefore, it is necessary to validate each of fuzzy partitions after the cluster analysis. Cluster validity refers to the problem whether a given fuzzy partition fits to the data all. The clustering algorithm always tries to find the best fit for a fixed number of clusters and the parameterized cluster shapes. However this does not mean that even the best fit is meaningful at all. Either the number of clusters might be wrong or the cluster shapes might not correspond to the groups in the data, if the data can be grouped in a meaningful way at all. In this study, several clustering indexes were used and tested for different values of both cluster number (*c*) and to examine their adequacy in analyzing of traffic accidents. These indexes are *Partition Coefficient (PC), Classification Entropy (CE), Partition Index (SC), Separation Index (S), Xie and Beni's Index (XB) and Dunn's Index (DI)*.

*Partition Coefficient (PC)* measures the amount of "overlapping" between two Fuzzy clusters (Bezdek, 1981). The disadvantage of this index is lack of direct connection to properties of the data. The optimal number of cluster is at the maximum value and the range of this index is [1/c, 1].

$$PC(c) = \frac{1}{N} \sum\_{i=1}^{c} \sum\_{k=1}^{N} \left( u\_{ik} \right)^2 \tag{11}$$

*Classification Entropy (CE)* measures the fuzziness of the cluster partition. The range of CE is [0, log *a c*( ) ] and optimal number of cluster is at minimum value.

$$CE(c) = -\frac{1}{N} \sum\_{i=1}^{c} \sum\_{k=1}^{N} \mu\_{ik} \log\_{a} a u\_{ik} \tag{12}$$

*Partition Index (SC)* is the ratio of the sum compactness and separation of the clusters. It is a sum of individual cluster validity measures normalized through division by the fuzzy cardinality of each cluster. Comparing different partitions having equal of clusters, SC is useful index and a lower value of this index demonstrates a better partition.

$$\text{SCf}(\mathbf{c}) = \sum\_{i=1}^{c} \frac{\sum\_{k=1}^{N} (\mu\_{ik})^m \left\| \mathbf{x}\_k - \boldsymbol{\upsilon}\_i \right\|^2}{N\_i \sum\_{k=1}^{c} (\mu\_{ik})^m \left\| \boldsymbol{\upsilon}\_k - \boldsymbol{\upsilon}\_i \right\|^2} \tag{13}$$

*Separation Index (S)* uses a minimum distance separation for partition validity.

$$\text{SC}(c) = \frac{\sum\_{i=1}^{c} \sum\_{k=1}^{N} (u\_{ik})^2 \left\| \mathbf{x}\_k - \mathbf{v}\_i \right\|^2}{N \min\_{i,k} \left\| \mathbf{v}\_k - \mathbf{v}\_i \right\|^2} \tag{14}$$

*Xie and Beni's Index (XB)* aims to quantify the ratio of the total variation within clusters and separation of clusters. The optimal value of cluster is at minimum value of this index.

$$\text{SCf}(\mathbf{c}) = \frac{\sum\_{i=1}^{c} \sum\_{k=1}^{N} (u\_{ik})^m \left\| \mathbf{x}\_k - \boldsymbol{v}\_i \right\|^2}{N \min\_{i,k} \left\| \mathbf{x}\_k - \boldsymbol{v}\_i \right\|^2} \tag{15}$$

*Dunn's Index (DI)* is proposed to use the identification of compactness and separated cluster.

$$DI(\mathbf{c}) = \min\_{i \in \mathcal{C}} \left\{ \min\_{k \in \mathcal{C}} i \neq k \left| \frac{\min\_{\mathbf{x} \in \mathbb{C}\_{i, y \in \mathcal{C}} d} d(\mathbf{x}, y)}{\max\_{k \in \mathcal{C}} \left\{ \max\_{\mathbf{x}, y \in \mathcal{C}} d(\mathbf{x}, y) \right\}} \right| \right\} \tag{16}$$

#### **4. Study area and available data**

In this study, Denizli that is a medium sized city (current population is about 700000) of Turkey is considered. Traffic accident records for the years of 2004, 2005 and 2006 are used in analyzing accidents. The accident reports are provided by Local Police Department. All of the data and documents are taken from an ongoing research project. Following information are collected from the reports:


88 Fuzzy Logic – Emerging Technologies and Applications

partitions. Therefore, it is necessary to validate each of fuzzy partitions after the cluster analysis. Cluster validity refers to the problem whether a given fuzzy partition fits to the data all. The clustering algorithm always tries to find the best fit for a fixed number of clusters and the parameterized cluster shapes. However this does not mean that even the best fit is meaningful at all. Either the number of clusters might be wrong or the cluster shapes might not correspond to the groups in the data, if the data can be grouped in a meaningful way at all. In this study, several clustering indexes were used and tested for different values of both cluster number (*c*) and to examine their adequacy in analyzing of traffic accidents. These indexes are *Partition Coefficient (PC), Classification Entropy (CE), Partition Index (SC), Separation Index (S), Xie and Beni's Index (XB) and Dunn's Index (DI)*.

*Partition Coefficient (PC)* measures the amount of "overlapping" between two Fuzzy clusters (Bezdek, 1981). The disadvantage of this index is lack of direct connection to properties of the data. The optimal number of cluster is at the maximum value and the range of this index

> 1 1 <sup>1</sup> () ( ) *c N*

*i k PC c u N*

*Classification Entropy (CE)* measures the fuzziness of the cluster partition. The range of CE is

1 1 <sup>1</sup> ( ) log *c N*

*i k CE c u au N*

*Partition Index (SC)* is the ratio of the sum compactness and separation of the clusters. It is a sum of individual cluster validity measures normalized through division by the fuzzy cardinality of each cluster. Comparing different partitions having equal of clusters, SC is

1

*<sup>c</sup> <sup>N</sup> <sup>m</sup>*

 

1 1

( ) ( ) min

*c N*

,

,

*N xv* 

*Xie and Beni's Index (XB)* aims to quantify the ratio of the total variation within clusters and separation of clusters. The optimal value of cluster is at minimum value of this index.

> *c N m ik k i i k ik k i*

*Dunn's Index (DI)* is proposed to use the identification of compactness and separated cluster.

1 1

( ) ( ) min

*N vv* 

*ik k i i k ik k i*

( )

*N u vv*

*ik k i k <sup>c</sup> <sup>m</sup> <sup>i</sup> i ik k i <sup>k</sup>*

*u xv*

<sup>1</sup> <sup>1</sup> ( ) ( )

useful index and a lower value of this index demonstrates a better partition.

*Separation Index (S)* uses a minimum distance separation for partition validity.

[0, log *a c*( ) ] and optimal number of cluster is at minimum value.

*SC c*

*SC c*

*SC c*

2

(11)

(12)

2

2 2

*u xv*

*u xv*

2

2

2

2

(13)

(14)

(15)

*ik*

*ik a ik*

is [1/c, 1].


All of these data given above are recorded using first MS Excel. Then, coordinates of each accident point are determined using street definition system in MAPINFO software. The data from Excel data base including coordinates of the accident points are transferred to MAPINFO data base. This data base is constituted for accident analysis by inquiring different attribution of each accident. Thus, traffic accident can be evaluated from different points of view and the relations about reasons and results of accidents can be revealed by these analysis.

The data related to coordinates of accidents (locations) are used in cluster analysis. The Figure 1 shows sample processed data on Denizli city GIS map (Murat et al, 2008). The data are analyzed using k-means and fuzzy clustering approaches.

Fuzzy Clustering Approach for Accident Black Spot Centers Determination 91

**Objective Function**

Fig. 2. Variation value of objective function of FCM with change in the number of clusters

**Dead+Injured Type Accidents**

0246

**Number of Clusters**

Fig. 3. Variation value of objective function of FCM with change in the number of clusters

**ED+Injured Type Accidents**

0 5 10 15 **Number of Clusters**

**ED Type Accidents**

0 2 4 6 8 10 12 **Number of Clusters**

for ED and ED+Injured type accidents.

0 0,5 1 1,5 2 2,5 3 3,5 4

**Objective Function**

for Dead and Injured accidents.

**Objective Function**

Fig. 1. Sample processed traffic accident data on Denizli city map.

#### **5. Analysis of traffic accidents**

In clustering analysis, the observed scales of the variables must be transformed so that their ranges are comparable because the clustering methods are sensitive to scale differences. Therefore, the variables were rescaled between 0 and 1 using equation (18).

$$\text{Latitude}\tag{18}$$

$$\text{Latitude}\tag{19}$$

$$Y = \begin{pmatrix} X - X\_{\text{min}} \end{pmatrix} / \begin{pmatrix} X\_{\text{max}} - X\_{\text{min}} \end{pmatrix}\tag{10}$$

Longitude min max min *Y XX X X* ( )/( )

Where *Y* the feature at site is, *X and X* min max are the maximum and minimum of the feature within the data set. These rescaled characteristics were employed as the basis for classifying the traffic accidents. To determine the optimum the cluster number, sensitivity of the results from FCM algorithm to variation in the value of cluster numbers (*c*) is varied from 2 to 9 with increment of 1. The variations of objective function of Fuzzy C-means algorithm for Economically Damaged (ED) and ED+ injured accidents with change in the number of cluster ranging from 2 to 11 are shown in Figure 2. On the other hand, for the Dead and Injured accidents, Figure 3 shows the variations of objective function of FCM algorithm with change in the number of cluster ranging from 2 to 5.

It is seen in Figure 2 and 3 that the values of objective functions of FCM algorithm, in generally, decrease with increase in the number cluster. The optimal number of clusters in the data set is identified by using objective function and fuzzy cluster validation indexes. The variations of cluster indexes for Economically Damaged accidents given in section 2 with change in the number of cluster were calculated and given in Figure 4.

In clustering analysis, the observed scales of the variables must be transformed so that their ranges are comparable because the clustering methods are sensitive to scale differences.

Latitude min max min *Y XX X X* ( )/( ) (18)

Where *Y* the feature at site is, *X and X* min max are the maximum and minimum of the feature within the data set. These rescaled characteristics were employed as the basis for classifying the traffic accidents. To determine the optimum the cluster number, sensitivity of the results from FCM algorithm to variation in the value of cluster numbers (*c*) is varied from 2 to 9 with increment of 1. The variations of objective function of Fuzzy C-means algorithm for Economically Damaged (ED) and ED+ injured accidents with change in the number of cluster ranging from 2 to 11 are shown in Figure 2. On the other hand, for the Dead and Injured accidents, Figure 3 shows the variations of objective function of FCM

It is seen in Figure 2 and 3 that the values of objective functions of FCM algorithm, in generally, decrease with increase in the number cluster. The optimal number of clusters in the data set is identified by using objective function and fuzzy cluster validation indexes. The variations of cluster indexes for Economically Damaged accidents given in section 2

Fig. 1. Sample processed traffic accident data on Denizli city map.

Therefore, the variables were rescaled between 0 and 1 using equation (18).

algorithm with change in the number of cluster ranging from 2 to 5.

with change in the number of cluster were calculated and given in Figure 4.

**5. Analysis of traffic accidents** 

Longitude min max min *Y XX X X* ( )/( )

Fig. 2. Variation value of objective function of FCM with change in the number of clusters for ED and ED+Injured type accidents.

Fig. 3. Variation value of objective function of FCM with change in the number of clusters for Dead and Injured accidents.

Fuzzy Clustering Approach for Accident Black Spot Centers Determination 93

The data are also analyzed by conventional K-means clustering approach. In this analysis, seven clusters are obtained. Figure 6 depicts results of k-means clustering approach. Table 3 shows the coordinates of cluster centers and the number of accidents for the clusters

> 1 29,082 37,782 1303 2 29,07 37,774 648 3 29,089 37,787 1389 4 29,086 37,772 1349 5 29,097 37,779 1253 6 29,107 37,802 501 7 29,08 37,795 509 8 29,037 37,773 248 9 29,099 37,792 605 10 29,089 37,756 662 11 29,101 37,763 631 TOTAL 9098

Table 2. Coordinates of Cluster centers given by Fuzzy C-means clustering analysis

Table 3. Coordinates of Cluster centers given by conventional k-means analysis

It can be said that analysis of the fuzzy clustering approach has more details than the

1 29,085 37,787 2480 2 29,041 37,772 302 3 29,102 37,798 973 4 29,072 37,778 835 5 29,096 37,780 1589 6 29,095 37,760 1274 7 29,086 37,772 1645 TOTAL 9098

**Coordinates Number of X Y Accidents** 

**Coordinates Number of Accidents x Y** 

determined by conventional k-means clustering analysis.

**Cluster No** 

**Cluster No** 

conventional k-means clustering approach.

Fig. 4. Variations of cluster indexes with change in the number of cluster

The main drawback of PC is the monotonic decreasing with *c* and the lack of direct connection to the data. CE has the same problems: monotonic increasing with *c* and hardly detectable connection to the data structure. It is seen in Figure 4 that SC and S decrease with increase in the number of cluster. On the other hand, SC, S and XB indexes reaches the optimal value of number of cluster *c* = 10 and 11. For Economically Damaged(ED) traffic accident analysis, eleven clusters were chosen as the optimal number of cluster according to optimal values of objective function and validity indexes given in Figure 3 and 4. Table 2 exhibits the coordinates of cluster centers for ED and injured type accidents obtained from fuzzy cluster analysis (Murat and Sekerler, 2009). Similar procedure was carried out for ED+ Injured and Dead and Injured type accidents. Figure 5 shows the location of the corresponding fuzzy clusters for traffic accidents in Denizli city.

CE

S

0.20 0.40 0.60 0.80 1.00 1.20

1.0E-04 3.0E-04 5.0E-04 7.0E-04 9.0E-04

1.00E-06 8.01E-04 1.60E-03 2.40E-03 3.20E-03

DI

The main drawback of PC is the monotonic decreasing with *c* and the lack of direct connection to the data. CE has the same problems: monotonic increasing with *c* and hardly detectable connection to the data structure. It is seen in Figure 4 that SC and S decrease with increase in the number of cluster. On the other hand, SC, S and XB indexes reaches the optimal value of number of cluster *c* = 10 and 11. For Economically Damaged(ED) traffic accident analysis, eleven clusters were chosen as the optimal number of cluster according to optimal values of objective function and validity indexes given in Figure 3 and 4. Table 2 exhibits the coordinates of cluster centers for ED and injured type accidents obtained from fuzzy cluster analysis (Murat and Sekerler, 2009). Similar procedure was carried out for ED+ Injured and Dead and Injured type accidents. Figure 5 shows the location of the

2 3 4 5 6 7 8 9 10 11 Number of Cluster (c)

2 3 4 5 6 7 8 9 10 11 Number of Cluster (c)

2 3 4 5 6 7 8 9 10 11 Number of Cluster (c)

0.40 0.50 0.60 0.70 0.80

0.60 1.20 1.80 2.40 3.00 3.60 4.20 4.80

8.0 12.0 16.0 20.0 24.0 28.0 32.0

XB

SC

PC

2 3 4 5 6 7 8 9 10 11 Number of Cluster (c)

2 3 4 5 6 7 8 9 10 11 Number of Cluster (c)

2 3 4 5 6 7 8 9 10 11 Number of Cluster (c)

Fig. 4. Variations of cluster indexes with change in the number of cluster

corresponding fuzzy clusters for traffic accidents in Denizli city.

The data are also analyzed by conventional K-means clustering approach. In this analysis, seven clusters are obtained. Figure 6 depicts results of k-means clustering approach. Table 3 shows the coordinates of cluster centers and the number of accidents for the clusters determined by conventional k-means clustering analysis.


Table 2. Coordinates of Cluster centers given by Fuzzy C-means clustering analysis


Table 3. Coordinates of Cluster centers given by conventional k-means analysis

It can be said that analysis of the fuzzy clustering approach has more details than the conventional k-means clustering approach.

Fuzzy Clustering Approach for Accident Black Spot Centers Determination 95

As seen on Figure 6, the centers obtained are similar to that obtained by fuzzy clustering approach. But fuzzy clustering approach provided four more clusters comparing to conventional k-means clustering approach. One of the important cluster (center named Ucgen) that has the biggest number of accident is not defined by k-means clustering

Total numbers of accidents are defined in both clustering analysis approaches. But the distributions of accidents are different for k-means and fuzzy c-means clustering approaches. This is come from the number of clusters and difference about the analysis.

Using cluster analysis, different types of traffic accidents are analyzed and three types of clusters are carried out as four, seven and eleven clusters respectively. Following table shows the common points that can be considered as black spots for three types of clusters. These points are also determined as the center of each cluster. As seen on Table 3, the

Location of black spots has an importance in analysis. It should be considered as urban sections and rural areas. But it is difficult to determine a strict line for clustering accidents. Some accidents location can be defined in more than one region or cluster. Therefore, fuzzy clustering approach is preferred. The results show that, Fuzzy clustering approach provided four more black spot centers comparing to k-means clustering approach. Three of them are

approach. But it is defined by fuzzy c-means clustering approach.

Fig. 6. Clusters obtained by K-means clustering approach.

number of accidents certified the black spots centers determined.

located in urban areas and one of them is in rural areas.

**6. Results and discussion** 

Fig. 5. The location of the corresponding fuzzy clusters for traffic accidents in Denizli city (a) for 11 clusters, (b) for 4 clusters.

Fig. 5. The location of the corresponding fuzzy clusters for traffic accidents in Denizli city (a)

for 11 clusters, (b) for 4 clusters.

As seen on Figure 6, the centers obtained are similar to that obtained by fuzzy clustering approach. But fuzzy clustering approach provided four more clusters comparing to conventional k-means clustering approach. One of the important cluster (center named Ucgen) that has the biggest number of accident is not defined by k-means clustering approach. But it is defined by fuzzy c-means clustering approach.

Total numbers of accidents are defined in both clustering analysis approaches. But the distributions of accidents are different for k-means and fuzzy c-means clustering approaches. This is come from the number of clusters and difference about the analysis.

Fig. 6. Clusters obtained by K-means clustering approach.

#### **6. Results and discussion**

Using cluster analysis, different types of traffic accidents are analyzed and three types of clusters are carried out as four, seven and eleven clusters respectively. Following table shows the common points that can be considered as black spots for three types of clusters. These points are also determined as the center of each cluster. As seen on Table 3, the number of accidents certified the black spots centers determined.

Location of black spots has an importance in analysis. It should be considered as urban sections and rural areas. But it is difficult to determine a strict line for clustering accidents. Some accidents location can be defined in more than one region or cluster. Therefore, fuzzy clustering approach is preferred. The results show that, Fuzzy clustering approach provided four more black spot centers comparing to k-means clustering approach. Three of them are located in urban areas and one of them is in rural areas.

Fuzzy Clustering Approach for Accident Black Spot Centers Determination 97

One of the different black spot is determined as 25. Cadde. This area is an industrial area that has many roads and intersections. The traffic composition includes heavy and light vehicle traffic flows are seen in this area. Most of the accidents are seen at intersections and all of them are controlled by isolated systems. One of the serious problems is related to

One of the main advantages of fuzzy cluster analysis is to handle the problem in an easiest and practical way. The conventional approaches take very long time and require many trials

Actually, most of reasons of problems occurred in all of these black spots are similar. These are high traffic density, non-optimized signal timing, inconvenient pedestrian crossings, and aggressive driving (caused by non-optimized control), geometric design faults (for weaving areas, taper design etc), inconvenient lane use and lane changing, excessive speed etc. Solutions for these problems can be achieved by developing some policies and intervene the system considering international standards for design. But sustainable solution can be found

The fuzzy clustering approach presented in this study can be used in determination of black spots instead of conventional approaches and traffic safety policies can be developed considering detailed analysis of these black spots. The fuzzy clustering approach can also be used for analyzing other related effective factors on traffic accidents and very interesting

The findings of this research can be used for investigation of different effects on traffic accident occurrence considering characteristics of black spots and centers. Safety levels of black spots can be determined by this way. Some countermeasures can be developed using safety levels of black spots. On the other hand, the risk analysis can be made in detail in these centers and priorities of investment planning can be defined considering level of safety risk. The fuzzy clustering analysis can be extended considering other characteristics (such as accident type, occurrence type etc.) of black spots. Therefore, definition of black spots can be

This research was supported by The Scientific and Technical Research Council of Turkey (TUBITAK) under project number 105G090. Part of the analysis presented is made by Mr. Alper Şekerler during preparation of his MSc. dissertation. These supports are appreciated.

Abdel-Aty M., Radwan E, (2000). Modelling traffic accident occurrence and involvement,

Abdel-Aty M.,Pange, A., (2007). Crash data analysis: Collective vs. individual crash level

design of intersections especially some uncontrolled intersections.

by generalizing and improving "*traffic concept*" in the society.

*Accident Analysis and Prevention* 32, 633-642.

approach*, Journal of Safety Research,* 38, 581–587

results may be obtained based on these analysis.

for the analysis.

**7. Conclusion** 

reviewed after these analyses.

**8. Acknowledgement** 

**9. References** 

The black spots that are determined by cluster analysis are examined in detail regarding types of accident occurrence. The geometric and physical conditions of black spots are also examined in detail and the results obtained are summarized as follow.


Table 3. The common black spots determined by cluster analysis

The first black spot, Ucgen Intersection, is one of the most important intersections in Denizli city center. The main arterials from Ankara, İzmir and Antalya cities are connected at this point. Average Annual Daily Traffic volume of this intersection is very high and congested traffic conditions are seen in peak hours. The Antalya road arm has some problems occurred by geometric design. There is not enough weaving area from the previous intersection for the vehicles that wants to change the lanes in this arm. Most of accidents are occurred because of this fault. Another important problem is related to pedestrian crossings. The pedestrians do not obey the rules while crossing the street.

Karayollar Intersection is determined as the second black spot. The main problem of this intersection is also related to geometric design. This intersection has five approaches. Therefore optimizing signal timing is very hard. Main reasons of accidents in this intersection are related to high speed and sight distance. The speed reduction and monitoring systems can reduce number of accidents and accident severity.

Cnar is another important intersection of the city. This intersection is served most of the daily traffic circulating in the city. There are some problems about optimizing signal timings. On the other hand, some drivers ride as aggressive drivers and cause traffic accidents. There is serious pedestrian traffic in this area and traffic signal is designed as filter for vehicles and pedestrians. Traffic safety problems are seen, because of the design and can be solved by re-calculating the intersection signal timings and changing phase plans.

The main problems in Kiremitci intersection is related to intersection geometry and aggressive drivers. The problem can be solved by re-designing and optimizing signal timings.

One of the different black spot is determined as 25. Cadde. This area is an industrial area that has many roads and intersections. The traffic composition includes heavy and light vehicle traffic flows are seen in this area. Most of the accidents are seen at intersections and all of them are controlled by isolated systems. One of the serious problems is related to design of intersections especially some uncontrolled intersections.

One of the main advantages of fuzzy cluster analysis is to handle the problem in an easiest and practical way. The conventional approaches take very long time and require many trials for the analysis.

Actually, most of reasons of problems occurred in all of these black spots are similar. These are high traffic density, non-optimized signal timing, inconvenient pedestrian crossings, and aggressive driving (caused by non-optimized control), geometric design faults (for weaving areas, taper design etc), inconvenient lane use and lane changing, excessive speed etc. Solutions for these problems can be achieved by developing some policies and intervene the system considering international standards for design. But sustainable solution can be found by generalizing and improving "*traffic concept*" in the society.

The fuzzy clustering approach presented in this study can be used in determination of black spots instead of conventional approaches and traffic safety policies can be developed considering detailed analysis of these black spots. The fuzzy clustering approach can also be used for analyzing other related effective factors on traffic accidents and very interesting results may be obtained based on these analysis.

#### **7. Conclusion**

96 Fuzzy Logic – Emerging Technologies and Applications

The black spots that are determined by cluster analysis are examined in detail regarding types of accident occurrence. The geometric and physical conditions of black spots are also

Ucgen 1 229 17 1 Karayollar 46 4 2 Cinar 1 86 1 3 Kiremitci 25 0 4 Yeni Adliye 27 6 5 İstasyon 1 107 12 6 Sevindik 93 8 7 Emniyet 1 76 9 8 Ulus 94 4 9 Hastane-M.Efendi 50 1 10 25. cadde 1 200 26 11

Type of Accident Cluster Dead+Injured No

ED+Injured Accidents

Economically Damaged

(ED) Accidents

examined in detail and the results obtained are summarized as follow.

Total 5 1033 88

monitoring systems can reduce number of accidents and accident severity.

The first black spot, Ucgen Intersection, is one of the most important intersections in Denizli city center. The main arterials from Ankara, İzmir and Antalya cities are connected at this point. Average Annual Daily Traffic volume of this intersection is very high and congested traffic conditions are seen in peak hours. The Antalya road arm has some problems occurred by geometric design. There is not enough weaving area from the previous intersection for the vehicles that wants to change the lanes in this arm. Most of accidents are occurred because of this fault. Another important problem is related to pedestrian crossings. The

Karayollar Intersection is determined as the second black spot. The main problem of this intersection is also related to geometric design. This intersection has five approaches. Therefore optimizing signal timing is very hard. Main reasons of accidents in this intersection are related to high speed and sight distance. The speed reduction and

Cnar is another important intersection of the city. This intersection is served most of the daily traffic circulating in the city. There are some problems about optimizing signal timings. On the other hand, some drivers ride as aggressive drivers and cause traffic accidents. There is serious pedestrian traffic in this area and traffic signal is designed as filter for vehicles and pedestrians. Traffic safety problems are seen, because of the design and can be solved by re-calculating the intersection signal timings and changing phase

The main problems in Kiremitci intersection is related to intersection geometry and aggressive drivers. The problem can be solved by re-designing and optimizing signal

Table 3. The common black spots determined by cluster analysis

pedestrians do not obey the rules while crossing the street.

Accidents

Intersection or Road Section (Black Spot)

plans.

timings.

The findings of this research can be used for investigation of different effects on traffic accident occurrence considering characteristics of black spots and centers. Safety levels of black spots can be determined by this way. Some countermeasures can be developed using safety levels of black spots. On the other hand, the risk analysis can be made in detail in these centers and priorities of investment planning can be defined considering level of safety risk. The fuzzy clustering analysis can be extended considering other characteristics (such as accident type, occurrence type etc.) of black spots. Therefore, definition of black spots can be reviewed after these analyses.

#### **8. Acknowledgement**

This research was supported by The Scientific and Technical Research Council of Turkey (TUBITAK) under project number 105G090. Part of the analysis presented is made by Mr. Alper Şekerler during preparation of his MSc. dissertation. These supports are appreciated.

#### **9. References**

Abdel-Aty M., Radwan E, (2000). Modelling traffic accident occurrence and involvement, *Accident Analysis and Prevention* 32, 633-642.

Abdel-Aty M.,Pange, A., (2007). Crash data analysis: Collective vs. individual crash level approach*, Journal of Safety Research,* 38, 581–587

**6** 

*Brazil* 

**Adaptive Security Policy Using** 

Ines Brosso1 and Alessandro La Neve2 *1Faculty of Computing and Informatics,* 

 *Mackenzie Presbyterian University, Sao Paulo,* 

 *2Department of Electrical Engineering, Centro Universitário da FEI, SP,* 

**User Behavior Analysis and Human** 

At present, security policy, to be effective, is primarily focused on people, being very rigid at

The security policy does not need to be rigid: rather it should be adaptable to the user

Analysis of human behavior, therefore, is the basis for an adaptive security policy. The behavior analysis of a person can be verified by a set of rules, which consider the variables that can influence human behavior, based on the information acquired about the environment, space, time, equipment, hardware and software. This information is used to analyze behavioral evidences about people, and establishes if it is possible to believe or not in the user. Therefore, according to the user behavior, levels of trust are released, which are based on the rules that were previously established for the parameters that are necessary to

The adaptive security policy based on user behavior analysis is the basis for the information

However, to achieve the whole security target in computing, and related technologies, it is necessary not only to have the most updated core technologies or security policies, but also to have the capacity to perform the analyses of the user behavior and the security environment. This work, in the context of computer security, uses the operant and conditioning behavior defined by Skinner (1991), which rewards a response of an individual

The Skinner Theory may be very interesting to be used in Information Security Management Systems. In operant behavior, the environment is modified and produces consequences that are working on it again, changing the likelihood of a future similar occurrence. Operant

this, and only later it cares about security attack attempts.

establish the evidences of behavioral trust, in its different degrees.

until he is conditioned to associate the need for action.

conditioning is a mechanism for learning a new behavior.

security management, when it comes to understanding the needs of users.

**1. Introduction** 

behavior.

 **Elements of Information Security** 


## **Adaptive Security Policy Using User Behavior Analysis and Human Elements of Information Security**

Ines Brosso1 and Alessandro La Neve2 *1Faculty of Computing and Informatics, Mackenzie Presbyterian University, Sao Paulo, 2Department of Electrical Engineering, Centro Universitário da FEI, SP, Brazil* 

#### **1. Introduction**

98 Fuzzy Logic – Emerging Technologies and Applications

Abdel-Aty, M. (2003). Analysis of driver injury severity levels at multiple locations using

Bezdek, J. C. (1981)., *Pattern Recognition with Fuzzy Objective Function Algorithms*, Plenum,

Bezdek, J. C.,(1973). *Fuzzy mathematics in pattern classification*., Ph.D. dissertation, Cornell

Dunn, J. C., (1974). A fuzzy relative of the ISODATA process and its use in detecting

Grubesic, T.H. (2006). On The Application of Fuzzy Clustering for Crime Hot Spot

Kamalasudhan A, Mitra, S., Huang, B., Chin, H., C., (2000). An Analysis Of Expressways

Murat, Y.Ş., Frat, M., Altun, S. (2008). Analysis of Traffic Accidents Using Fuzzy Clustering

Murat, Y.Ş., Şekerler, A., (2009). Use of Clustering Approach in Traffic Accident Data

Ng, K.S., Hung, W.T., Wong, W.G., (2002). An algorithm for assessing the risk of traffic

Saploglu, M., Karasahin, M. (2006). Urban Traffic Accident Analysis by using Geographic

Şekerler, A., (2008). *Analysis of Traffic Accident Data using Clustering Approac*h, Master of

Wang, Y., Nihan, N. (2004). Estimating the risk of collisions between bicycles and motor vehicles at signalized intersections, *Accident Analysis and Prevention* 36, 313–321.

and Geographical Information Systems, *10th International Conference on Application of Advanced Technologies in Transportation*, May 27- 31, Athens GREECE , 2008.

Modelling, *Technical Journal of Turkish Chamber of Civil Engineers*, Vol. 20, No 3, July

Information System, *Journal Of Engineering Sciences*, Pamukkale University,

Science Thesis, Pamukkale University, Institute of Natural and Applied Sciences,

compact, well-separated clusters., *Journal of Cybernetics*, 3(3), 32-57.

Detection, *Journal of Quantitative Criminology*, Vol. 22, No. 1, 77-105. http://gisdevelopment.net./application/urban/products/index.htm. 18

ordered probit models, *Journal of Safety Research* 34, 597– 603.

New York.

University, Ithaca, NY.

(Proceeding CD)

Accident in Singapore available from

2009, p 4759-4777. (in Turkish)

113 p, Denizli, Turkey. (in Turkish)

accident", *Journal of Safety Research*, 33, 387-410.

Engineering College, Vol. 12, 3, 321-332. (in Turkish)

At present, security policy, to be effective, is primarily focused on people, being very rigid at this, and only later it cares about security attack attempts.

The security policy does not need to be rigid: rather it should be adaptable to the user behavior.

Analysis of human behavior, therefore, is the basis for an adaptive security policy. The behavior analysis of a person can be verified by a set of rules, which consider the variables that can influence human behavior, based on the information acquired about the environment, space, time, equipment, hardware and software. This information is used to analyze behavioral evidences about people, and establishes if it is possible to believe or not in the user. Therefore, according to the user behavior, levels of trust are released, which are based on the rules that were previously established for the parameters that are necessary to establish the evidences of behavioral trust, in its different degrees.

The adaptive security policy based on user behavior analysis is the basis for the information security management, when it comes to understanding the needs of users.

However, to achieve the whole security target in computing, and related technologies, it is necessary not only to have the most updated core technologies or security policies, but also to have the capacity to perform the analyses of the user behavior and the security environment. This work, in the context of computer security, uses the operant and conditioning behavior defined by Skinner (1991), which rewards a response of an individual until he is conditioned to associate the need for action.

The Skinner Theory may be very interesting to be used in Information Security Management Systems. In operant behavior, the environment is modified and produces consequences that are working on it again, changing the likelihood of a future similar occurrence. Operant conditioning is a mechanism for learning a new behavior.

Adaptive Security Policy Using User

environment and the user.

application, often called the session.

analysis, according to the following steps:

historical behavioral information.

two phases:

applications.

Behavior Analysis and Human Elements of Information Security 101

The user behavior is a combination of n dimensions. The user behavior analysis uses the context variables of the environment and the trust, the concept that we human beings have regarding a person, and it is based on the behavior and reputation of a person. In this way, the environmental variables model of the user's behavior, in a conditioning process, uses the

 **User -** User is a person who has been approved in an authentication process to have access to software applications in a specific area of computer networks and wireless. **Context -** Any information that can be used to characterize the situation of the

 **Environment –** *Environmental technology*: the infrastructure needed in a specific area of computer networks, wired and wireless. *Technological environment:* local capture information, from behavior of users that interact with software and hardware

 **Time interval -** The interval of time that elapses from the initial instant the user makes his identification on a software application access to the moment he exits the

 **Behavior** - The behavior is the set of actions and responses that enable the intent of a person and the technological environment; or actions that a user performs when

The focus of Behavior Analysis, as proposed by Skinner (1991), is currently applied in this work, for effective analysis of user behavior, to fulfill the requirements of user behavior

Behavioral analysis is based on evidence of user behavior and comparison with information stored in databases of the same behavioral history. The behavioral analysis is carried out in

The first is to compare the information obtained at the time the user interacts with the

 The second phase is to verify the existence, or absence, of behavioral constraints that can collaborate with the analysis, to convey or not to the user authentication.

The capture of user behavioral information in the environment is done analyzing some human elements of information security. It is closely associated with such characteristically human activities as philosophy, science, language, mathematics and art, and is normally considered to be a definitive characteristic of human nature. Human nature refers to the

interacting with the software applications and the technological environment. **Trust** - Concept assigned to the user, which may vary according to the behavioral analysis of it. Based on the evidence of user behavior it is possible to determine the level of trust to give him. Trust is an abstract concept that expresses the belief that one has in the sincerity or authenticity of another person. The trust level of the person user is according to the analysis of his behavior. The concept of trust is a characteristic common to human beings, and is directly related to the perception, knowledge and reputation of a person about another. *Trust Restriction* -It refers to the behavior of the user that runs off the expected normality. A restriction may be due to a sequence of not recommended transactions, values or places different from usual, or others. The

restriction of trust can be used in user adaptive security policy.

concepts of user, context, environment, time interval, behavior and trust, as follows:

When the organism answers an environmental stimulation, and the consequences of its reply are rewarded, the probability of similar answers increases; when the consequences are punitive, such probability diminishes. People associate experiences they have gone through to similar ones they may find in life: in this case they adopt the same behavior and repeat their actions.

The methodology for the preparation of this book chapter consisted of literature review, research on historical, social and psychological aspects of the Behavioral Theory, and the development of an Intelligent Security System. Studies and research on mathematical methods for handling trust information, fuzzy-logic, Information security management, context-aware computing and adaptive security policies, were also necessary.

In order to integrate information security management, based on adaptive security policy, with user behavior analysis, a deep understanding of Behavioral Theory, with historical, social and psychological aspects are necessary. At the same time, it also important to have full expertise in mathematical methods for handling information about people behavior, context-aware computing and self-aware computing systems, which can be the basis for an adaptive security policy based on user behavioral analysis.

This work was based on a doctoral thesis (Brosso, 2006) and research in the area.

### **2. Adaptive security policy**

One of the more challenging questions in security is how to specify an adaptive security policy. The security policy does not need to be rigid, but it should be adaptable to the user behavior. In this context, this work exploits security aspects, user behavior analysis, trust in behavior, and biometric technologies to be the base of an adaptive security policy. The goal for specifying adaptive security is twofold:


The security policies for computing resources must match the security policies of the organizations that use them; therefore, computer security policies must be adaptable to meet the changing security environment of their user-base. The term "adaptive security" is intended to indicate that security policies and mechanisms can change in some automated or semi-automated way in response to events.

#### **3. USER behavior analysis**

The user behavior analysis helps to define an adaptive security policy to the information security management. Human behavior is based on contextual information, which is retrieved by behavioral history, history of behavior reinforcement and conduct of the person to interact with the environment immediately (Witter, 2005).The scientific analysis of human behavior starts with the knowledge of the environment and isolation of the parts of an event to determine the characteristics and the dimensions of the occasion where the behavior occurs, and to define the changes that were produced in response to the environment, space, time and opportunities.

When the organism answers an environmental stimulation, and the consequences of its reply are rewarded, the probability of similar answers increases; when the consequences are punitive, such probability diminishes. People associate experiences they have gone through to similar ones they may find in life: in this case they adopt the same behavior and repeat

The methodology for the preparation of this book chapter consisted of literature review, research on historical, social and psychological aspects of the Behavioral Theory, and the development of an Intelligent Security System. Studies and research on mathematical methods for handling trust information, fuzzy-logic, Information security management,

In order to integrate information security management, based on adaptive security policy, with user behavior analysis, a deep understanding of Behavioral Theory, with historical, social and psychological aspects are necessary. At the same time, it also important to have full expertise in mathematical methods for handling information about people behavior, context-aware computing and self-aware computing systems, which can be the basis for an

One of the more challenging questions in security is how to specify an adaptive security policy. The security policy does not need to be rigid, but it should be adaptable to the user behavior. In this context, this work exploits security aspects, user behavior analysis, trust in behavior, and biometric technologies to be the base of an adaptive security policy. The goal

to provide an umbrella guide to decide which future events, actions, or responses are

to allow new security goals to be stated, in order to initiate system responses to enforce

The security policies for computing resources must match the security policies of the organizations that use them; therefore, computer security policies must be adaptable to meet the changing security environment of their user-base. The term "adaptive security" is intended to indicate that security policies and mechanisms can change in some automated

The user behavior analysis helps to define an adaptive security policy to the information security management. Human behavior is based on contextual information, which is retrieved by behavioral history, history of behavior reinforcement and conduct of the person to interact with the environment immediately (Witter, 2005).The scientific analysis of human behavior starts with the knowledge of the environment and isolation of the parts of an event to determine the characteristics and the dimensions of the occasion where the behavior occurs, and to define the changes that were produced in response to the environment, space,

context-aware computing and adaptive security policies, were also necessary.

This work was based on a doctoral thesis (Brosso, 2006) and research in the area.

adaptive security policy based on user behavioral analysis.

**2. Adaptive security policy** 

that policy, if necessary.

**3. USER behavior analysis** 

time and opportunities.

for specifying adaptive security is twofold:

permitted in the current policy; and

or semi-automated way in response to events.

their actions.

The user behavior is a combination of n dimensions. The user behavior analysis uses the context variables of the environment and the trust, the concept that we human beings have regarding a person, and it is based on the behavior and reputation of a person. In this way, the environmental variables model of the user's behavior, in a conditioning process, uses the concepts of user, context, environment, time interval, behavior and trust, as follows:


The focus of Behavior Analysis, as proposed by Skinner (1991), is currently applied in this work, for effective analysis of user behavior, to fulfill the requirements of user behavior analysis, according to the following steps:

Behavioral analysis is based on evidence of user behavior and comparison with information stored in databases of the same behavioral history. The behavioral analysis is carried out in two phases:


The capture of user behavioral information in the environment is done analyzing some human elements of information security. It is closely associated with such characteristically human activities as philosophy, science, language, mathematics and art, and is normally considered to be a definitive characteristic of human nature. Human nature refers to the

Adaptive Security Policy Using User

than sense perceptions on their own.

in the field of logic.

**6. Logic** 

**4. Human elements** 

policy.

**5. Reason** 

Behavior Analysis and Human Elements of Information Security 103

Some Human Elements like reason, logic and trust help to analyze both the user behavior and to study a source of norms of conduct or ways of life to produce an adaptive security

Beer (1994) explains that reason is a term that refers to the capacity that human beings have to make sense of things, to establish and verify facts, and to change or justify practices, institutions and beliefs. The concept of reason is sometimes referred to as rationality and was considered to be of higher stature than other characteristics of human nature. Reason is associated with thinking, by which it flows from one idea to a related one. It is the means by which rational beings understand themselves thinking about truth and falsehood, and what is good or bad. Reason relies on mental processes, related to the primary perceptive ability of humans, which gathers the perceptions of different senses and defines the order of the things that are perceived. Reasoning, in an argument, is valid if the argument's conclusion comes to be true when the premises, or the reasons given to support that conclusion, are true. If such reasoned conclusions are originally built only upon a foundation of sense perceptions, on the other hand, conclusions reached in this way are considered more certain

Gilovich (1991 ) explains that psychologists and cognitive scientists have attempted to study and explain how people reason, what cognitive and neural processes are engaged, and how cultural factors affect the inferences that people draw to determine whether or not

Experiments investigate how people make inferences about factual situations, hypothetical possibilities, probabilities, and counterfactual situations, and how it influences the human behavior. Humans have certain invariant structures, such as coherence and ability to establish relationships that give rise to the categories of reason that are structured in touch with reality, so that reason becomes a result of the action of biological maturation and the environment. Reason is a consideration that explains or justifies some behavior of humans

Gottwald and Hajek (2005) wrote that, in contrast with traditional logic theory, where binary sets have two-valued logic, true or false, fuzzy logic variables may have a truth value, that ranges in degree from 0 to 1. In logic, a many-valued logic or multi-valued logic

Fuzzy logic is a form of many-valued logic; it deals with reasoning that is approximate rather than fixed and exact and it has been extended to handle the concept of partial truth, where the truth value may range from completely true to completely false. While variables in mathematics usually take numerical values, in fuzzy logic applications, the non-numeric

people are capable of rational thoughts in various different circumstances.

is a propositional calculus in which there are more than two truth values.

linguistic variables are often used to facilitate the expression of rules and facts.

In this work, relevant human elements like reason, logic and trust, are used in this study.

distinguishing characteristics, including ways of thinking, feeling and acting, that humans tend to have naturally.


Table 1. Steps of analysis of user behavior

The questions concerning these characteristics, what causes them and how this causation works, and how fixed human nature is, are amongst the oldest and most important questions in western philosophy. These questions have important implications particularly in ethics, politics and theology.

The user behavior analysis will also be concentrated on understanding how we can trust in the user.

In this work, relevant human elements like reason, logic and trust, are used in this study.

#### **4. Human elements**

Some Human Elements like reason, logic and trust help to analyze both the user behavior and to study a source of norms of conduct or ways of life to produce an adaptive security policy.

#### **5. Reason**

102 Fuzzy Logic – Emerging Technologies and Applications

distinguishing characteristics, including ways of thinking, feeling and acting, that humans

Step 2: Observe the behavior Observe the behavior, the response and what

develop his behavior.

behavior.

The questions concerning these characteristics, what causes them and how this causation works, and how fixed human nature is, are amongst the oldest and most important questions in western philosophy. These questions have important implications particularly

The user behavior analysis will also be concentrated on understanding how we can trust in

Define the target of the behavior to be analyzed, to measure the frequency with which it occurs, or capture the variable and compare it with the restrictions and historical behavior in databases.

will happen, or wait for the action of the user interaction in a given period of time, capturing the information received and waiting for the application to send a stimulus to the user to

Record the rate of occurrence of the behavior, (frequency), in order to measure the behavior occurred throughout the process, and stores it

Where appropriate, introduce the experimental variable. It is applied to introduce a new tool for the user, such as a new code of access or a

Compare the frequency of behavior before and

occurrence of response. Currently, restrictions are compared to the user's past behavior. Thus, it can be said that the environment and both the

after the experimental variable or the

virtual and physical space establish the conditions for a certain behavior.

in the user behavior database.

new field of application.

Observe the behavior in terms of triple contingency, which is the expression used to say that it will see the context, the response and what will happen; or wait for the action of the user interaction with the application software in a given period of time, capture the information received and wait for the application to send the user a stimulus to provoke a certain

**Steps of analysis of user behavior Description** 

tend to have naturally.

triple contingency

Step 4: Behavior frequency

variable

behavior

the user.

Step 5: Introduce the experimental

Step 6: Compare the frequency of

Table 1. Steps of analysis of user behavior

in ethics, politics and theology.

Step 1: Target of the Behavior

Step 3: Observe the behavior in terms of

Beer (1994) explains that reason is a term that refers to the capacity that human beings have to make sense of things, to establish and verify facts, and to change or justify practices, institutions and beliefs. The concept of reason is sometimes referred to as rationality and was considered to be of higher stature than other characteristics of human nature. Reason is associated with thinking, by which it flows from one idea to a related one. It is the means by which rational beings understand themselves thinking about truth and falsehood, and what is good or bad. Reason relies on mental processes, related to the primary perceptive ability of humans, which gathers the perceptions of different senses and defines the order of the things that are perceived. Reasoning, in an argument, is valid if the argument's conclusion comes to be true when the premises, or the reasons given to support that conclusion, are true. If such reasoned conclusions are originally built only upon a foundation of sense perceptions, on the other hand, conclusions reached in this way are considered more certain than sense perceptions on their own.

Gilovich (1991 ) explains that psychologists and cognitive scientists have attempted to study and explain how people reason, what cognitive and neural processes are engaged, and how cultural factors affect the inferences that people draw to determine whether or not people are capable of rational thoughts in various different circumstances.

Experiments investigate how people make inferences about factual situations, hypothetical possibilities, probabilities, and counterfactual situations, and how it influences the human behavior. Humans have certain invariant structures, such as coherence and ability to establish relationships that give rise to the categories of reason that are structured in touch with reality, so that reason becomes a result of the action of biological maturation and the environment. Reason is a consideration that explains or justifies some behavior of humans in the field of logic.

#### **6. Logic**

Gottwald and Hajek (2005) wrote that, in contrast with traditional logic theory, where binary sets have two-valued logic, true or false, fuzzy logic variables may have a truth value, that ranges in degree from 0 to 1. In logic, a many-valued logic or multi-valued logic is a propositional calculus in which there are more than two truth values.

Fuzzy logic is a form of many-valued logic; it deals with reasoning that is approximate rather than fixed and exact and it has been extended to handle the concept of partial truth, where the truth value may range from completely true to completely false. While variables in mathematics usually take numerical values, in fuzzy logic applications, the non-numeric linguistic variables are often used to facilitate the expression of rules and facts.

Adaptive Security Policy Using User

behavior and adjusting the trust in the user.

behavior.

the levels of trust.

historical behavior.

static and dynamic.

Behavior Analysis and Human Elements of Information Security 105

generated by the user. Trust level of the user is given according to the analysis of his

According to the user behavior, trust levels are released, to let the user have access to the application software. These levels, however, are not determined by clear and cut rules, that reflect a classification that can easily and universally be applied to human actions, but rather they must reflect the shady, undefined, and yet evident, characteristics of human behavior. With the increase of behavior information, a more efficient support for behavior evidences analysis is generated, and the system continues performing the evidences analysis of the

Trust can change depending on the user, the localization, the time and the trust restrictions. With trust based on behavioral information and in the environment context information, it is possible to infer a minimum value for the initial trust, and, along the time, based on the behavior analysis and in the trust restrictions, the system will change

The heuristics adopted to define the initial trust can be defined according to the user activity at a particular moment, its location, the time that the behavior currently occurs, and his

 1st stage – Since there is not enough behavior information, it is attributed a minimum level of trust and, at the end, it accounts and stores the captured information. 2nd stage - In the subsequent accesses, when the user interaction increases, a verification is done, at first, in the trust restrictions database: if there are no restrictions, it compares the current behavior with the behavior information database, but if there are any changes in behavior, the alarm is triggered, the new behavior is stored, trust is

According to the user behavior, levels of trust are released, based on the rules that were previously established for the parameters which help to establish the evidences of

Thus, it can be said that the environment and both the virtual and physical space establish the conditions for a certain behavior. It is necessary, therefore, to define some entities, used in behavior analysis, a set of context variables *{who, where, when, what, why, how, rest}*, that is,

The set of context variables *{who, where, when, what, why, how, rest}* helps to decide what information is relevant to a system. However it is necessary to analyze the requirements and model the necessary information that each dimension can provide, since, in general, there is a tendency to develop a context model in which the user overrides associated problems, and this is a generalization to classify the context in temporal aspects, both

To capture the behavior means to store the information of the behavioral variables *{who, where, when, what, why, how and rest}*, in a data structure represented by the matrix of user behavior. Given the uncertainty and doubt, it is often necessary to take decisions based on

The attribution of the subsequent levels of trust is processed in two stages:

re-calculated and security mechanisms are trigged.

behavioral trust, in its different degrees.

the evidence of the user behavior, as in table 2.

Logical systems in general are based on some formalized language which includes a notion of well-formed formula, and then they are determined either semantically or syntactically. A logical system that is semantically determined means that one has a notion of interpretation or model, each such interpretation every well-formed formula has some (truth) value or represents a function into the set of (truth) values. It means, furthermore, that one has a notion of validity for well formed formulas and, based upon it, also a natural entailment relation between sets of well formed formulas and single formulas (or sometimes also whole sets of formulas).

That a logical system is syntactically determined means that one has a notion of proof and of provable formula, i.e. of (formal) theorem, as well as a notion of derivation from a set of premises. From a philosophical, especially epistemological point of view, the semantic aspect of (classical) logic is more basic than the syntactic one, because semantic ideas mainly determine what are suitable syntactic versions of the corresponding (system of) logic.

Fuzzy set theory defines fuzzy operators on fuzzy sets. The problem in applying this is that the appropriate fuzzy operator may not be known. For this reason, fuzzy logic usually uses IF-THEN rules, or constructs the equivalent ones, such as fuzzy associative matrices. There are also other operators, more linguistic in nature, called hedges that can be applied. These are generally adverbs such as "very", or "somewhat", which modify the meaning of a set using a mathematical formula.

Zadeh (1968) proposed that in mathematical logics, there are several formal systems of "fuzzy logic"; most of them belong to the so-called t-norm fuzzy logics. The notions of a "decidable subset" and "recursively enumerable subset" are basic ones for classical mathematics and classical logic. Ω denotes the set of rational numbers in [0,1]. A fuzzy subset s : S [0,1] of a set S is recursively enumerable, if a recursive map h : S×N Ω exists such that, for every x in S, the function h(x,n) is increasing with respect to *n* and s(x) = lim h(x,n); *s* is decidable if both *s* and its complement *–s* are recursively enumerable. An extension of such a theory to the general case of the L-subsets is proposed in Gerla (2006).

One of the main interests of the fuzzy logic theory is that many parameters can be taken into account since no mathematical modeling is required. This applies to the plant control area, but also to forecasting, decision support and risk scoring. On the other hand, Ang (2003) refers to neuro-fuzzy as combinations of artificial neural networks and fuzzy logic, the Neuro-Fuzzy Logic Rules and fuzzy sets are optimized by training strategies originated from neural network theory. In logic, trust is a dimensional, or multidimensional, variable, because it is possible to trust, not trust or have no evidence to attribute trust over an interval of time.

#### **7. Trust**

Trust is an abstract concept, and it reveals a belief in the sincerity or authenticity of one person in relation to another. Trust, a concept that we human beings have regarding a person, is based on the behavior and reputation of a person. This concept is not a unique and indivisible attribute that can be given to someone, and it is not the dichotomy of trust or not trust: on the contrary, it can be graded, and therefore it is dimensional and measurable. Trust levels may be stipulated based on the user behavioral analysis and on trust restrictions

Logical systems in general are based on some formalized language which includes a notion of well-formed formula, and then they are determined either semantically or syntactically. A logical system that is semantically determined means that one has a notion of interpretation or model, each such interpretation every well-formed formula has some (truth) value or represents a function into the set of (truth) values. It means, furthermore, that one has a notion of validity for well formed formulas and, based upon it, also a natural entailment relation between sets of well formed formulas and single formulas (or sometimes also whole

That a logical system is syntactically determined means that one has a notion of proof and of provable formula, i.e. of (formal) theorem, as well as a notion of derivation from a set of premises. From a philosophical, especially epistemological point of view, the semantic aspect of (classical) logic is more basic than the syntactic one, because semantic ideas mainly determine what are suitable syntactic versions of the corresponding (system of)

Fuzzy set theory defines fuzzy operators on fuzzy sets. The problem in applying this is that the appropriate fuzzy operator may not be known. For this reason, fuzzy logic usually uses IF-THEN rules, or constructs the equivalent ones, such as fuzzy associative matrices. There are also other operators, more linguistic in nature, called hedges that can be applied. These are generally adverbs such as "very", or "somewhat", which modify the meaning of a set

Zadeh (1968) proposed that in mathematical logics, there are several formal systems of "fuzzy logic"; most of them belong to the so-called t-norm fuzzy logics. The notions of a "decidable subset" and "recursively enumerable subset" are basic ones for classical mathematics and classical logic. Ω denotes the set of rational numbers in [0,1]. A fuzzy subset s : S [0,1] of a set S is recursively enumerable, if a recursive map h : S×N Ω exists such that, for every x in S, the function h(x,n) is increasing with respect to *n* and s(x) = lim h(x,n); *s* is decidable if both *s* and its complement *–s* are recursively enumerable. An extension of such a theory to the general case of the L-subsets is proposed in Gerla (2006). One of the main interests of the fuzzy logic theory is that many parameters can be taken into account since no mathematical modeling is required. This applies to the plant control area, but also to forecasting, decision support and risk scoring. On the other hand, Ang (2003) refers to neuro-fuzzy as combinations of artificial neural networks and fuzzy logic, the Neuro-Fuzzy Logic Rules and fuzzy sets are optimized by training strategies originated from neural network theory. In logic, trust is a dimensional, or multidimensional, variable, because it is possible to trust, not trust or have no evidence to attribute trust over an interval

Trust is an abstract concept, and it reveals a belief in the sincerity or authenticity of one person in relation to another. Trust, a concept that we human beings have regarding a person, is based on the behavior and reputation of a person. This concept is not a unique and indivisible attribute that can be given to someone, and it is not the dichotomy of trust or not trust: on the contrary, it can be graded, and therefore it is dimensional and measurable. Trust levels may be stipulated based on the user behavioral analysis and on trust restrictions

sets of formulas).

using a mathematical formula.

logic.

of time.

**7. Trust** 

generated by the user. Trust level of the user is given according to the analysis of his behavior.

According to the user behavior, trust levels are released, to let the user have access to the application software. These levels, however, are not determined by clear and cut rules, that reflect a classification that can easily and universally be applied to human actions, but rather they must reflect the shady, undefined, and yet evident, characteristics of human behavior. With the increase of behavior information, a more efficient support for behavior evidences analysis is generated, and the system continues performing the evidences analysis of the behavior and adjusting the trust in the user.

Trust can change depending on the user, the localization, the time and the trust restrictions. With trust based on behavioral information and in the environment context information, it is possible to infer a minimum value for the initial trust, and, along the time, based on the behavior analysis and in the trust restrictions, the system will change the levels of trust.

The heuristics adopted to define the initial trust can be defined according to the user activity at a particular moment, its location, the time that the behavior currently occurs, and his historical behavior.

The attribution of the subsequent levels of trust is processed in two stages:


According to the user behavior, levels of trust are released, based on the rules that were previously established for the parameters which help to establish the evidences of behavioral trust, in its different degrees.

Thus, it can be said that the environment and both the virtual and physical space establish the conditions for a certain behavior. It is necessary, therefore, to define some entities, used in behavior analysis, a set of context variables *{who, where, when, what, why, how, rest}*, that is, the evidence of the user behavior, as in table 2.

The set of context variables *{who, where, when, what, why, how, rest}* helps to decide what information is relevant to a system. However it is necessary to analyze the requirements and model the necessary information that each dimension can provide, since, in general, there is a tendency to develop a context model in which the user overrides associated problems, and this is a generalization to classify the context in temporal aspects, both static and dynamic.

To capture the behavior means to store the information of the behavioral variables *{who, where, when, what, why, how and rest}*, in a data structure represented by the matrix of user behavior. Given the uncertainty and doubt, it is often necessary to take decisions based on

Adaptive Security Policy Using User

alert signals are triggered.

Fig. 1. The increase of trust

Fig. 2. The loss of trust

**8. The information security** 

The loss of confidence grows fast, as it can be seen in figure 2.

Behavior Analysis and Human Elements of Information Security 107

distrust. If there are any differences, confidence in the user will be decreased, and even access and continuity of operation are liable to be blocked. In case of indications of changes, in the user's behavior, if there are uncertainties and divergences, security mechanisms and

There is an uncertainty in the allocation of trust, however, because not always the complement of the expressed trust is distrust. Along the time, and in accordance with the behavior analysis, the user trust level can be subject to variations, and thus, it is necessary to interact with the user, to determine evidences so as to increase or to decrease trust in the user. Considering the definitions of reason, logic and trust, we can see that people use logic,

Information security means protecting information and information systems from unauthorized access, use, disclosure, disruption, modification, perusal, inspection,

deduction, and inductions, to reach conclusions that they think are true.


evidences, which are not always accurate. In these cases, trust should be used, which is a staff metric criterion adopted to evaluate evidence.

Table 2. Variables of the evidence of the user

The concept of trust is a characteristic common to humans, and is directly related to perception, knowledge and reputation that a person has about the other. According to Dempster (1967) and Shaffer (1976), a measure of confidence, in a universe set X that represents the total amount of confidence in the evidence of a particular set of circumstances, which varies between 0 and 1, is given by the function: Cf (x): P (X) ← [0, 1].

 Based on the evidences of the behavior, the application software establishes if it trusts the user with values in the interval (mC, mD), where mC is the initial minimum trust and mD is the initial minimum diffidence.

The confidence (Cf), the diffidence (Df) and the uncertainty (If) express all the possibilities of trust attribution to a user, in this form:Cf + Df + If = 1. The uncertainty If is defined as: (If) = 1- (Cf + Df).

If Bj is a user behavior, the System, based on the evidences of the behavior, establishes if it trusts the user with values in the interval (mC, mD), where mC is the initial minimum trust and mD is the initial minimum diffidence. The system checks the uncertainty of confidence, which is given by: If (Bj) = 1 - (mC + mD). If the behavior Bj is considered normal, confidence is assigned to the user, linearly and slowly.

If there is uncertainty, safety mechanisms, like sensors that capture the user information, can be triggered and compare it with the existing one in databases. If there is an unusual behavior, behavioral constraints are generated, decreasing the confidence and increasing distrust. If there are any differences, confidence in the user will be decreased, and even access and continuity of operation are liable to be blocked. In case of indications of changes, in the user's behavior, if there are uncertainties and divergences, security mechanisms and alert signals are triggered.

Fig. 1. The increase of trust

106 Fuzzy Logic – Emerging Technologies and Applications

evidences, which are not always accurate. In these cases, trust should be used, which is a

Identification. It identifies the user in an application software session. It helps User-behavior analysis, in classifying users according to their access patterns. This is useful for personalization, targeted advertising,

Space Locality: It identifies either the location where the user is, or the

device address that the user is accessing. It is of user interest, determining whether users in the same geographical region tend to receive or request similar notification and browsing content. For analysis, it should be defined a notification message to be locally shared, if at least two users in the same cluster receive the notification.

When Time. It identifies the current time that the user is in a software

What Qualification. It identifies what the user is doing in a software

Why Intention. It means the action of the user to the stimulus received. How Method. It justifies the user repetitive activities in a software application

Rest Restrictions. It identifies either the user behavior or the software

The concept of trust is a characteristic common to humans, and is directly related to perception, knowledge and reputation that a person has about the other. According to Dempster (1967) and Shaffer (1976), a measure of confidence, in a universe set X that represents the total amount of confidence in the evidence of a particular set of circumstances, which varies between 0 and 1, is given by the function: Cf (x): P (X) ← [0, 1]. Based on the evidences of the behavior, the application software establishes if it trusts the user with values in the interval (mC, mD), where mC is the initial minimum trust and mD is

The confidence (Cf), the diffidence (Df) and the uncertainty (If) express all the possibilities of trust attribution to a user, in this form:Cf + Df + If = 1. The uncertainty If is defined as: (If) =

If Bj is a user behavior, the System, based on the evidences of the behavior, establishes if it trusts the user with values in the interval (mC, mD), where mC is the initial minimum trust and mD is the initial minimum diffidence. The system checks the uncertainty of confidence, which is given by: If (Bj) = 1 - (mC + mD). If the behavior Bj is considered normal,

If there is uncertainty, safety mechanisms, like sensors that capture the user information, can be triggered and compare it with the existing one in databases. If there is an unusual behavior, behavioral constraints are generated, decreasing the confidence and increasing

staff metric criterion adopted to evaluate evidence.

Who

Where

**Variables Description** 

priority, and capacity planning.

application session.

application session.

application restrictions.

confidence is assigned to the user, linearly and slowly.

session.

Table 2. Variables of the evidence of the user

the initial minimum diffidence.

1- (Cf + Df).

The loss of confidence grows fast, as it can be seen in figure 2.

Fig. 2. The loss of trust

There is an uncertainty in the allocation of trust, however, because not always the complement of the expressed trust is distrust. Along the time, and in accordance with the behavior analysis, the user trust level can be subject to variations, and thus, it is necessary to interact with the user, to determine evidences so as to increase or to decrease trust in the user. Considering the definitions of reason, logic and trust, we can see that people use logic, deduction, and inductions, to reach conclusions that they think are true.

#### **8. The information security**

Information security means protecting information and information systems from unauthorized access, use, disclosure, disruption, modification, perusal, inspection,

Adaptive Security Policy Using User

Fig. 3. The Intelligent Security System

Behavior Analysis and Human Elements of Information Security 109

The intelligent security system should be prepared not to anticipate every possible action that may be taken in the future, but to be flexible enough to adapt itself more easily to the changes that will certainly come, identifying technological trends and knowing more about

Neural networks are systems that try to make use of some of the known or expected organizing principles of the human brain. Neural networks can be used if training data is available. It is not necessary to have a mathematical model of the problem of interest, and

The neural function system has to learn what the behavioral changes of the user are, and incorporates them in the system, for a future fuzzy treatment. The fuzzy system evaluates, within an historical and behavioral perspective, human behavior, reflecting the perception or feeling that man or society have in relation to behavioral attitudes. Based on these

On the other hand the solution obtained from the learning process usually cannot be interpreted. Neural networks and fuzzy systems have certain advantages over classical methods, especially when vague data or prior knowledge are involved. However, their applicability suffered from several weaknesses of the individual models. Therefore, combinations of neural networks with fuzzy systems have been proposed, where both models

human behavior, which will always be the crucial aspect of security.

there is no need to provide any form of prior knowledge.

attitudes weights are qualified and assigned.

complement each other.

recording or destruction. The terms information security, computer security and information assurance are often interrelated and share the common goals for protecting the confidentiality, integrity and availability of data regardless of the form the data may take electronic, print, mobile or other forms. Computer security can focus on ensuring the availability and correct operation of a computer system without concern for the information stored or processed by the computer.

For the individual, information security has a significant effect on privacy, which is viewed very differently in different cultures. Governments, military corporations, financial institutions, hospitals, and private businesses amass a great deal of confidential information about their employees, customers, products, research, and financial status. Most of this information is now collected, processed and stored on electronic computers and transmitted to other computers across networks.

Should confidential information about a business customer, or a new product line, fall in the hands of a competitor, such breach in security could lead to losses in business, law suits or even bankruptcy of companies. Protecting confidential information is a business requirement, and in many cases also an ethical and legal requirement.

Information Security is composed of three main parts, namely hardware, software and communications, to identify and apply information security industry standards, as mechanisms of protection and prevention, at three levels or layers: physical, personal and organizational. Procedures or policies are essentially implemented to tell people (administrators, users and operators) how to use products to ensure information security within the organizations.

The field of information security has many areas including: securing network(s) and allied infrastructure, securing applications and databases, security testing, information systems auditing, business continuity planning, digital forensics science, security systems, etc. In this work we study an intelligent security system in collaboration with the information security.

#### **9. An intelligent security system**

It is here presented a study about an intelligent security system that uses an adaptive security policy using User Behavior Analysis and Human Elements of Information Security.

Figure 3 shows the mechanism that is used when the user accesses the computer: the intelligent security system verifies and analyzes the user behavior. This system is based on the fuzzy logic theory and must be able to acquire information about the environment, space, time, equipment, hardware, software and user behavior analysis, established for the variables *{who, where, when, what, why, how, rest}*. Fuzzy logic considers truth values, that are a value indicating the relation of a proposition to truth, ranging from 0 to 1 – but conceptually distinct, due to different interpretations.

The intelligent system proposes that, based on the evidences of the user behavior, it is possible to trust or not trust the user. Levels of trust are released, according to the user behavior and the rules that were previously established for the parameters which help to establish the evidences of behavioral trust, interacting with the environment information, so as to keep trust levels updated.

recording or destruction. The terms information security, computer security and information assurance are often interrelated and share the common goals for protecting the confidentiality, integrity and availability of data regardless of the form the data may take electronic, print, mobile or other forms. Computer security can focus on ensuring the availability and correct operation of a computer system without concern for the information

For the individual, information security has a significant effect on privacy, which is viewed very differently in different cultures. Governments, military corporations, financial institutions, hospitals, and private businesses amass a great deal of confidential information about their employees, customers, products, research, and financial status. Most of this information is now collected, processed and stored on electronic computers and transmitted

Should confidential information about a business customer, or a new product line, fall in the hands of a competitor, such breach in security could lead to losses in business, law suits or even bankruptcy of companies. Protecting confidential information is a business

Information Security is composed of three main parts, namely hardware, software and communications, to identify and apply information security industry standards, as mechanisms of protection and prevention, at three levels or layers: physical, personal and organizational. Procedures or policies are essentially implemented to tell people (administrators, users and operators) how to use products to ensure information security

The field of information security has many areas including: securing network(s) and allied infrastructure, securing applications and databases, security testing, information systems auditing, business continuity planning, digital forensics science, security systems, etc. In this work we study an intelligent security system in collaboration with the information security.

It is here presented a study about an intelligent security system that uses an adaptive security policy using User Behavior Analysis and Human Elements of Information Security. Figure 3 shows the mechanism that is used when the user accesses the computer: the intelligent security system verifies and analyzes the user behavior. This system is based on the fuzzy logic theory and must be able to acquire information about the environment, space, time, equipment, hardware, software and user behavior analysis, established for the variables *{who, where, when, what, why, how, rest}*. Fuzzy logic considers truth values, that are a value indicating the relation of a proposition to truth, ranging from 0 to 1 – but

The intelligent system proposes that, based on the evidences of the user behavior, it is possible to trust or not trust the user. Levels of trust are released, according to the user behavior and the rules that were previously established for the parameters which help to establish the evidences of behavioral trust, interacting with the environment information, so

requirement, and in many cases also an ethical and legal requirement.

stored or processed by the computer.

to other computers across networks.

within the organizations.

**9. An intelligent security system** 

as to keep trust levels updated.

conceptually distinct, due to different interpretations.

Fig. 3. The Intelligent Security System

The intelligent security system should be prepared not to anticipate every possible action that may be taken in the future, but to be flexible enough to adapt itself more easily to the changes that will certainly come, identifying technological trends and knowing more about human behavior, which will always be the crucial aspect of security.

Neural networks are systems that try to make use of some of the known or expected organizing principles of the human brain. Neural networks can be used if training data is available. It is not necessary to have a mathematical model of the problem of interest, and there is no need to provide any form of prior knowledge.

The neural function system has to learn what the behavioral changes of the user are, and incorporates them in the system, for a future fuzzy treatment. The fuzzy system evaluates, within an historical and behavioral perspective, human behavior, reflecting the perception or feeling that man or society have in relation to behavioral attitudes. Based on these attitudes weights are qualified and assigned.

On the other hand the solution obtained from the learning process usually cannot be interpreted. Neural networks and fuzzy systems have certain advantages over classical methods, especially when vague data or prior knowledge are involved. However, their applicability suffered from several weaknesses of the individual models. Therefore, combinations of neural networks with fuzzy systems have been proposed, where both models complement each other.

Adaptive Security Policy Using User

cannot usually be interpreted.

output, exemplified in Figure 4.

Fig. 4. The structure of Fuzzy Logic

ability of a neural network to optimize its parameters.

their reputation as alternative approaches to information processing.

uncertainty.

Behavior Analysis and Human Elements of Information Security 111

The modeling of single neurons and the called "learning rules" for modifying synaptic weights can be used in neural networks if training data are available. It is not necessary to have a mathematical model of the problem of interest, and there is no need to provide any form of prior knowledge. On the other hand the solution obtained from the learning process

Although there are some approaches to extract rules from neural networks, most neural network architectures are black boxes. The fuzzy set theory makes possible that an object or a case belong to a set only to a certain degree that includes similarity, preference, and

The idea of combining fuzzy systems and neural networks is to design an architecture that uses a fuzzy system to represent knowledge in an interpretable manner and the learning

A combination can constitute an interpretable model that is capable of learning and can use problem-specific prior knowledge. Neural networks and fuzzy systems have established

Neuro-fuzzy models are neural networks with intrinsic fuzzy logic abilities, where the weights of the neurons in the network define the premise and consequent parameters of a fuzzy inference system. Premise parameters determine the shape and size of the input membership functions, whilst consequent parameters determine the characteristics of the

The proposed intelligent system adopts neuro-fuzzy logic because of its capacity to use past experiences and learn new ones. Weights can be attributed in the fuzzyfication process, according to the rules that were previously established for the variables {*who, where, when, what, why, how, rest}*, which help to establish the evidences of behavioral trust, in its different degrees.

The fuzzyfication of qualifiers should consider the intrinsic characteristics of the variables, according to specific application in which they are used. A financial institution, for instance, might consider the depositor of a bank for the variable *who*. Some qualifiers that could be associated to this variable might be: new or ancient (client), young or aged (person) , and others that the financial institution might find interesting or important in order to better define their clients.

A neuro-fuzzy system can feed the user behavioral database continuously, interacting with the fuzzyfication mechanism, so as to keep trust levels updated according to the user behavior, in a more accurate and faithful way, and to give more robustness to the system based on user behavior. The fuzzy set theory, as used here ,is based on if-then rules. The antecedent of a rule consists of fuzzy descriptions of input values, and the consequent defines a possibly fuzzy output value for the given input. The benefits of these fuzzy systems lie in the suitable knowledge representation.

According to the user behavior, levels of trust are released, to have access to the application software. These levels, however, are not determined by clear and cut rules, that reflect a classification that can easily and universally be applied to human actions, but rather they must reflect the shady, undefined, and yet evident, characteristics of human behavior.

In fact a major difficulty arises when actual values must be attributed to the parameter "*m"*( minimum), which is used in the Cf(x) and Df(x) functions, because of the subjectivity involved. Since there are no behavioral rules that can strictly be applied to people, no matter what their personal characteristics are, a more suitable mathematical tool, like softcomputing, should be used. The adoption of fuzzy logic, as a way of thinking, and then subsequently neuro-fuzzy systems, with learning possibilities, turned out to be a very interesting and effective solution.

Fuzzy logic allows that weights be attributed, based both on the designer's system needs and the experience drawn from historical events. With this in mind, and at hand, fuzzyfication rules, which are necessary to quantify vague and undefined qualifications, can be implemented resorting to the user behavior database, so as to find the optimal solution in each case, or set of cases.

The dynamism with which users access the system, constantly requires that the authentication system, as mentioned before, continuously revise, and possibly recalculate, trust levels to be released to the user, based on the behavioral history that the user himself continuously builds.

Neural networks are systems that try to make use of some of the known or expected organizing principles of the human brain. They consist of a number of independent, simple processors: the neurons. These neurons communicate with each other via weighted connections.

The proposed intelligent system adopts neuro-fuzzy logic because of its capacity to use past experiences and learn new ones. Weights can be attributed in the fuzzyfication process, according to the rules that were previously established for the variables {*who, where, when, what, why, how, rest}*, which help to establish the evidences of behavioral trust,

The fuzzyfication of qualifiers should consider the intrinsic characteristics of the variables, according to specific application in which they are used. A financial institution, for instance, might consider the depositor of a bank for the variable *who*. Some qualifiers that could be associated to this variable might be: new or ancient (client), young or aged (person) , and others that the financial institution might find interesting or important in order to better

A neuro-fuzzy system can feed the user behavioral database continuously, interacting with the fuzzyfication mechanism, so as to keep trust levels updated according to the user behavior, in a more accurate and faithful way, and to give more robustness to the system based on user behavior. The fuzzy set theory, as used here ,is based on if-then rules. The antecedent of a rule consists of fuzzy descriptions of input values, and the consequent defines a possibly fuzzy output value for the given input. The benefits of these fuzzy

According to the user behavior, levels of trust are released, to have access to the application software. These levels, however, are not determined by clear and cut rules, that reflect a classification that can easily and universally be applied to human actions, but rather they must reflect the shady, undefined, and yet evident, characteristics of human behavior.

In fact a major difficulty arises when actual values must be attributed to the parameter "*m"*( minimum), which is used in the Cf(x) and Df(x) functions, because of the subjectivity involved. Since there are no behavioral rules that can strictly be applied to people, no matter what their personal characteristics are, a more suitable mathematical tool, like softcomputing, should be used. The adoption of fuzzy logic, as a way of thinking, and then subsequently neuro-fuzzy systems, with learning possibilities, turned out to be a very

Fuzzy logic allows that weights be attributed, based both on the designer's system needs and the experience drawn from historical events. With this in mind, and at hand, fuzzyfication rules, which are necessary to quantify vague and undefined qualifications, can be implemented resorting to the user behavior database, so as to find the optimal solution in

The dynamism with which users access the system, constantly requires that the authentication system, as mentioned before, continuously revise, and possibly recalculate, trust levels to be released to the user, based on the behavioral history that the user himself

Neural networks are systems that try to make use of some of the known or expected organizing principles of the human brain. They consist of a number of independent, simple processors: the neurons. These neurons communicate with each other via weighted

in its different degrees.

define their clients.

systems lie in the suitable knowledge representation.

interesting and effective solution.

each case, or set of cases.

continuously builds.

connections.

The modeling of single neurons and the called "learning rules" for modifying synaptic weights can be used in neural networks if training data are available. It is not necessary to have a mathematical model of the problem of interest, and there is no need to provide any form of prior knowledge. On the other hand the solution obtained from the learning process cannot usually be interpreted.

Although there are some approaches to extract rules from neural networks, most neural network architectures are black boxes. The fuzzy set theory makes possible that an object or a case belong to a set only to a certain degree that includes similarity, preference, and uncertainty.

The idea of combining fuzzy systems and neural networks is to design an architecture that uses a fuzzy system to represent knowledge in an interpretable manner and the learning ability of a neural network to optimize its parameters.

A combination can constitute an interpretable model that is capable of learning and can use problem-specific prior knowledge. Neural networks and fuzzy systems have established their reputation as alternative approaches to information processing.

Neuro-fuzzy models are neural networks with intrinsic fuzzy logic abilities, where the weights of the neurons in the network define the premise and consequent parameters of a fuzzy inference system. Premise parameters determine the shape and size of the input membership functions, whilst consequent parameters determine the characteristics of the output, exemplified in Figure 4.

Fig. 4. The structure of Fuzzy Logic

Adaptive Security Policy Using User

Fig. 6. Trust variation.

the trust restrictions.

in table 1.

the user behavior, in a more accurate and faithful way.

localization, the time and the trust restrictions.

Behavior Analysis and Human Elements of Information Security 113

It is therefore necessary to count on a mechanism with learning ability, such as a neuro system, that is able to give support to the fuzzyfication rules, according to the user behavioral changes. This will, not only update the user behavioral database, but it will interact with the fuzzyfication mechanism, so as to keep trust levels updated ,according to

With the increase of behavior information, a more efficient support for behavior evidences analysis is generated, and the system continues performing the evidences analysis of the behavior and adjusting the trust in the user. The trust can change depending on the user, the

The system attributes trust based on behavioral information and in the context information from the environment, and so, it is possible to infer a minimum value for the initial trust, and along the time the system will change the trust, based on the behavior analysis and in

For the Intelligent System, "behavior" is the action of the user to the stimulus received, and "to capture the behavior" means to store the information of behavioral variables (*who, where, when, what, why and rest)* in a data structure represented by the matrix of user behavior.

The human behavior is uncertain and unpredictable. It is not algorithmic. It is based on the individual history of the person and groups. Therefore, the individual experience of the person should be considered in this analysis. The greater the amount of captured information, the better the analysis behavior will be. The user behavior is a combination of *n*  dimensions. The focus of Behavior Analysis proposed by Skinner (2003) is currently applied to the system for effective analysis of user behavior according to the steps that were defined

Fig. 5. The architectural of the Intelligent Security System with variables

Fig. 5. The architectural of the Intelligent Security System with variables

It is therefore necessary to count on a mechanism with learning ability, such as a neuro system, that is able to give support to the fuzzyfication rules, according to the user behavioral changes. This will, not only update the user behavioral database, but it will interact with the fuzzyfication mechanism, so as to keep trust levels updated ,according to the user behavior, in a more accurate and faithful way.

With the increase of behavior information, a more efficient support for behavior evidences analysis is generated, and the system continues performing the evidences analysis of the behavior and adjusting the trust in the user. The trust can change depending on the user, the localization, the time and the trust restrictions.

Fig. 6. Trust variation.

The system attributes trust based on behavioral information and in the context information from the environment, and so, it is possible to infer a minimum value for the initial trust, and along the time the system will change the trust, based on the behavior analysis and in the trust restrictions.

For the Intelligent System, "behavior" is the action of the user to the stimulus received, and "to capture the behavior" means to store the information of behavioral variables (*who, where, when, what, why and rest)* in a data structure represented by the matrix of user behavior.

The human behavior is uncertain and unpredictable. It is not algorithmic. It is based on the individual history of the person and groups. Therefore, the individual experience of the person should be considered in this analysis. The greater the amount of captured information, the better the analysis behavior will be. The user behavior is a combination of *n*  dimensions. The focus of Behavior Analysis proposed by Skinner (2003) is currently applied to the system for effective analysis of user behavior according to the steps that were defined in table 1.

Adaptive Security Policy Using User

Behavior Analysis and Human Elements of Information Security 115

So, according to the user behavior, levels of trust were released, to access the application software. Weights were attributed in the fuzzyfication process, according to the rules that were previously established for the parameters *(who, where, when, what, why, rest)*, which

Therefore, with this approach, it was possible to define an adaptive security policy, based on

In future developments, the intelligent system for information security should be prepared, not to anticipate every possible action that may be taken, but to be adaptable enough to respond more rapidly to the changes that will certainly come. It should also be capable of identifying new technological trends and know more about human behavior, which will

Besides this, considering the steady and fast evolution of Information Technology and Communications in its manifold aspects, which are becoming more complex and sophisticated, it is necessary to think of a larger System, a Security Management System, that is not only robust enough to correspond to the current needs, but it may also be intelligent and prepared for the future, so as to guarantee to society the real benefits that

Ang, K. K., Quek, C., & Pasquier, M. (2003). "POPFNN-CRI(S): pseudo outer product based

Azzini, A.; Marrara, S.; Sassi, R.; Scotti, F. (2007) A fuzzy approach to multimodal biometric

Beer, Francis A., "Words of Reason", Political Communication 11 (Summer, 1994): 185-201. Brosso, I. (2006) *Users continuous authentication in computers networks* – Doctoral Thesis in

Brosso, I,; La Neve, A.; Bressan, G.; Ruggiero, W.V. (2010) A Continuous Authentication

Dempster, A. P. (1967) Upper and Lower Probabilities Induced by a Multi-valued Mapping,

Gerla, Giangiacomo (2006). "Effectiveness and Multivalued Logics". Journal of Symbolic

Gilovich, Thomas (1991), How We Know What Isn't So: The Fallibility of Human Reason in

Logic 71 (1): 137–162. doi:10.2178/jsl/1140641166. ISSN 0022-4812.

Everyday Life, New York: The Free Press, ISBN 0-02-911705-4

http://doi.ieeecomputersociety.org/10.1109/ARES.2010.63

*Annals of Mathematical Statistics*, Vol.38, pp.325-339.

fuzzy neural network using the compositional rule of inference and singleton fuzzyfier." IEEE Transactions on Systems, Man and Cybernetics, Part B, 33(6), 838-

authentication. In *Proceedings of the 11th International Conference on Knowledge-Based and Intelligent Information & Engineering Systems, KES'07*, Vietri sul Mare (SA), Italy,

Digital Systems at Polytechnic School of Sao Paulo University, Brazil, from http://www.teses.usp.br/teses/disponiveis/3/3141/tde-08122006-170242/en.php

System Based on User Behavior Analysis, *International Conference on Availability, Reliability and Security, International Conference* , pp. 380-385, Krakow, Poland, February 15-February 18, ISBN: 978-0-7695-3965-2, retrieved December 2010 from

help to establish the evidences of behavioral trust, in its different degrees.

the behavioral analysis of computer network users.

always be the crucial aspect of a security system.

Information Technology has to offer.

**11. References** 

849.

September.

Fig. 7. Trust variation with trust restrictions.

#### **10. Conclusion**

To establish the policy and mechanisms for an adaptive security system, which is intended to protect society and its institutions, it is fundamental to know and analyze more deeply, besides the different technical and organizational aspects of the system, human behavior, which is often neglected.

Human behavioral characteristics, in fact, are some very important components that have to be considered, since they are partly subjective , but they are also strongly influenced by the social group the individuals belongs to: they may be predictable, to a certain extent, but they are certainly not ascertainable algorithmically.

Therefore, the need of mathematical support, in the design of an adaptive security system, conveys to the adoption of a neuro-fuzzy system. Neuro-fuzzy systems have the necessary flexibility to use past experiences, which are not algorithmic, and learn new ones. The neuro-fuzzy system allows that the user behavioral database be continuously updated, interacting with the fuzzyfication mechanism, so as to keep trust levels updated ,according to the user behavior, in a more accurate and faithful way.

The implemented Intelligent System was validated with tests and simulations to authenticate a person's identity using behavior analysis and trust restrictions, which are the basis for an adaptive security system. It acquired information in the context that was submitted, and they were used as a basis for user behavior. The System, based on the evidences of the user behavior, established if the user could be trusted or not, and to what extent.

So, according to the user behavior, levels of trust were released, to access the application software. Weights were attributed in the fuzzyfication process, according to the rules that were previously established for the parameters *(who, where, when, what, why, rest)*, which help to establish the evidences of behavioral trust, in its different degrees.

Therefore, with this approach, it was possible to define an adaptive security policy, based on the behavioral analysis of computer network users.

In future developments, the intelligent system for information security should be prepared, not to anticipate every possible action that may be taken, but to be adaptable enough to respond more rapidly to the changes that will certainly come. It should also be capable of identifying new technological trends and know more about human behavior, which will always be the crucial aspect of a security system.

Besides this, considering the steady and fast evolution of Information Technology and Communications in its manifold aspects, which are becoming more complex and sophisticated, it is necessary to think of a larger System, a Security Management System, that is not only robust enough to correspond to the current needs, but it may also be intelligent and prepared for the future, so as to guarantee to society the real benefits that Information Technology has to offer.

#### **11. References**

114 Fuzzy Logic – Emerging Technologies and Applications

To establish the policy and mechanisms for an adaptive security system, which is intended to protect society and its institutions, it is fundamental to know and analyze more deeply, besides the different technical and organizational aspects of the system, human behavior,

Human behavioral characteristics, in fact, are some very important components that have to be considered, since they are partly subjective , but they are also strongly influenced by the social group the individuals belongs to: they may be predictable, to a certain extent, but they

Therefore, the need of mathematical support, in the design of an adaptive security system, conveys to the adoption of a neuro-fuzzy system. Neuro-fuzzy systems have the necessary flexibility to use past experiences, which are not algorithmic, and learn new ones. The neuro-fuzzy system allows that the user behavioral database be continuously updated, interacting with the fuzzyfication mechanism, so as to keep trust levels updated ,according

The implemented Intelligent System was validated with tests and simulations to authenticate a person's identity using behavior analysis and trust restrictions, which are the basis for an adaptive security system. It acquired information in the context that was submitted, and they were used as a basis for user behavior. The System, based on the evidences of the user behavior, established if the user could be trusted or not, and to what

Fig. 7. Trust variation with trust restrictions.

are certainly not ascertainable algorithmically.

to the user behavior, in a more accurate and faithful way.

**10. Conclusion** 

extent.

which is often neglected.


**Part 2** 

**Transportation and Communication**

